{ "source": "https://notes.mathforge.org/notes/published/HomePage", "puzzles": [ { "slug": "three-hexagons-on-a-circle", "name": "three hexagons on a circle", "title": "Three Hexagons on a Circle", "date": "2026-07-04", "statement": "Three regular hexagons. The smallest has area $6$. What’s the pink area?", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3mpsmxuhho222", "categories": [ "Shapes", "Transformations and Symmetry", "Circle Theorems", "Other Techniques" ], "techniques": [ "hexagon", "angles in the same segment", "symmetry", "invariance principle" ], "drawing": "three-hexagons-on-a-circle.lgf", "live": true }, { "slug": "a-triangle-inside-a-hexagon", "name": "a triangle inside a hexagon", "title": "A Triangle Inside a Hexagon", "date": "2026-05-30", "statement": "An equilateral triangle inside a regular hexagon. What’s the angle?", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3mn2spzcdmk25", "categories": [ "Shapes", "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "hexagon", "transformation", "invariance principle" ], "drawing": "a-triangle-inside-a-hexagon.lgf", "live": true }, { "slug": "a-semi-circle-and-a-quarter-circle", "name": "a semi-circle and a quarter circle", "title": "A Semi-Circle and a Quarter Circle", "date": "2026-03-29", "statement": "The two blue angles are equal. What’s the size of the orange angle?", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3mi772wdces2h", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "a-semi-circle-and-a-quarter-circle.lgf", "live": true }, { "slug": "seven-squares", "name": "seven squares", "title": "Seven Squares", "date": "2026-02-28", "statement": "Seven squares. What’s the angle?", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3mfvvp2krs22g", "categories": [ "Shapes", "Circle Theorems", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "seven-squares.lgf", "live": true }, { "slug": "six-squares-and-a-quarter-circle", "name": "six squares and a quarter circle", "title": "Six Squares and a Quarter Circle", "date": "2026-02-16", "statement": "Six squares and a quarter circle. The blue square has area $2$. What’s the yellow area?", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3mextvtqacc2b", "categories": [ "Circle Theorems", "Other Techniques" ], "techniques": [], "drawing": "six-squares-and-a-quarter-circle.lgf", "live": true }, { "slug": "two-hexagons-in-a-rectangle-ii", "name": "two hexagons in a rectangle ii", "title": "Two Hexagons in a Rectangle II", "date": "2026-02-07", "statement": "Two regular hexagons inside a rectangle. What fraction of the rectangle is shaded?", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3meb7kxny2k2j", "categories": [ "Measures" ], "techniques": [], "drawing": "two-hexagons-in-a-rectangle-ii.lgf" }, { "slug": "three-congruent-rectangles-vi", "name": "three congruent rectangles vi", "title": "Three Congruent Rectangles VI", "date": "2025-07-05", "statement": "The three rectangles are congruent. What fraction of the design is shaded?", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3lt7mbgldxs2s", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-congruent-rectangles-vi.lgf", "live": true }, { "slug": "four-quarter-circles-iii", "name": "four quarter circles iii", "title": "Four Quarter Circles III", "date": "2025-06-28", "statement": "Four quarter circles. What’s the area of the orange one?", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3lsnhbfsjrk2d", "categories": [ "Transformations and Symmetry" ], "techniques": [ "congruent" ], "drawing": "four-quarter-circles-iii.lgf", "live": true }, { "slug": "two-triangles-in-a-semi-circle", "name": "two triangles in a semi-circle", "title": "Two Triangles in a Semi-Circle", "date": "2025-06-21", "statement": "These triangles are congruent and isosceles. What’s the area of the semicircle?", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3ls4cjjrvuk2f", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-triangles-in-a-semi-circle.lgf", "live": true }, { "slug": "four-squares-x", "name": "four squares x", "title": "Four Squares X", "date": "2025-06-14", "statement": "Four squares. What’s the blue square’s area?", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3lrknviguck2i", "categories": [ "Shapes" ], "techniques": [], "drawing": "four-squares-x.lgf" }, { "slug": "four-squares-ix", "name": "four squares ix", "title": "Four Squares IX", "date": "2025-06-07", "statement": "Four Squares. What's the angle?", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3lqywcmno6s2a", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "four-squares-ix.lgf" }, { "slug": "three-regular-hexagons-and-a-semi-circle", "name": "three regular hexagons and a semi-circle", "title": "Three Regular Hexagons and a Semi-Circle", "date": "2025-05-31", "statement": "Three regular hexagons. What’s the diameter of the semicircle?", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3lqhnq7njg22r", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "three-regular-hexagons-and-a-semi-circle.lgf", "live": true }, { "slug": "four-quarter-circles-ii", "name": "four quarter circles ii", "title": "Four Quarter Circles II", "date": "2025-05-30", "statement": "Four quarter circles. What fraction is shaded?", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3lqewsscomk2g", "categories": [ "Measures", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "four-quarter-circles-ii.lgf", "live": true }, { "slug": "subdivided-triangle-ii", "name": "subdivided triangle ii", "title": "Subdivided Triangle II", "date": "2025-05-29", "statement": "What fraction of the triangle is shaded?", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3lqcsphprac2d", "categories": [ "Measures" ], "techniques": [], "drawing": "subdivided-triangle-ii.lgf", "live": true }, { "slug": "four-squares-xii", "name": "four squares xii", "title": "Four Squares XII", "date": "2024-02-25", "statement": "The three smaller squares are the same size. What’s the angle?", "categories": [ "Shapes", "Other Techniques" ], "techniques": [ "isosceles triangle", "invariance principle" ], "drawing": "four-squares-xii.lgf", "live": true }, { "slug": "four-squares-xi", "name": "four squares xi", "title": "Four Squares XI", "date": "2024-02-24", "statement": "Four squares. What’s the green area?", "categories": [ "Measures", "Transformations and Symmetry", "Circle Theorems", "Other Techniques" ], "techniques": [ "Pythagoras", "similarity", "transformation", "angle at the circumference is half that at the centre", "invariance principle" ], "drawing": "four-squares-xi.lgf", "live": true }, { "slug": "four-squares-and-an-isosceles-triangle", "name": "four squares and an isosceles triangle", "title": "Four Squares and an Isosceles Triangle", "date": "2023-08-13", "statement": "Four squares and an isosceles triangle. What’s the blue area?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "similarity" ], "drawing": "four-squares-and-an-isosceles-triangle.lgf" }, { "slug": "two-triangles-and-a-quarter-circle", "name": "two triangles and a quarter circle", "title": "Two Triangles and a Quarter Circle", "date": "2023-08-12", "statement": "The green triangles are congruent. What’s the angle?", "categories": [ "Circle Theorems" ], "techniques": [ "angle in a semi-circle" ], "drawing": "two-triangles-and-a-quarter-circle.lgf", "live": true }, { "slug": "two-squares-and-a-quarter-circle", "name": "two squares and a quarter circle", "title": "Two Squares and a Quarter Circle", "date": "2023-08-11", "statement": "The area of the red square is 12. What’s the total yellow area?", "categories": [ "Measures", "Other Techniques" ], "techniques": [], "drawing": "two-squares-and-a-quarter-circle.lgf", "live": true }, { "slug": "five-squares-ii", "name": "five squares ii", "title": "Five Squares II", "date": "2023-04-14", "statement": "What fraction of the total area is shaded?", "categories": [ "Shapes", "Transformations and Symmetry" ], "techniques": [ "triangle", "transformation" ], "drawing": "five-squares-ii.lgf", "live": true }, { "slug": "four-rectangles-and-a-hexagon", "name": "four rectangles and a hexagon", "title": "Four Rectangles and a Hexagon", "date": "2023-03-12", "statement": "What's the angle hidden inside this trophy made of four squares and a regular hexagon?", "categories": [ "Shapes", "Trigonometry" ], "techniques": [], "drawing": "four-rectangles-and-a-hexagon.lgf" }, { "slug": "two-quarter-circles-and-a-circle", "name": "two quarter circles and a circle", "title": "Two Quarter Circles and a Circle", "date": "2023-02-25", "statement": "The yellow circle has radius 4. What’s the total area of the two quarter circles?", "categories": [ "Measures", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "two-quarter-circles-and-a-circle.lgf", "live": true }, { "slug": "subdivided-hexagon-iv", "name": "subdivided hexagon iv", "title": "Subdivided Hexagon IV", "date": "2023-02-17", "statement": "What fraction of this regular hexagon is shaded?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "subdivided-hexagon-iv.lgf" }, { "slug": "a-semi-circle-and-a-quarter-circle-in-a-rectangle", "name": "a semi-circle and a quarter circle in a rectangle", "title": "A Semi-Circle and a Quarter Circle in a Rectangle", "date": "2023-02-16", "statement": "What’s the shaded area?", "categories": [ "Measures" ], "techniques": [], "drawing": "a-semi-circle-and-a-quarter-circle-in-a-rectangle.lgf" }, { "slug": "three-squares-viii", "name": "three squares viii", "title": "Three Squares VIII", "date": "2023-02-15", "statement": "Three squares. What’s the angle?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-squares-viii.lgf" }, { "slug": "three-lengths-in-a-semi-circle", "name": "three lengths in a semi-circle", "title": "Three Lengths in A Semi-Circle", "date": "2023-02-14", "statement": "What’s the area of this semicircle?", "categories": [ "Measures", "Circle Theorems" ], "techniques": [ "Pythagoras" ], "drawing": "three-lengths-in-a-semi-circle.lgf" }, { "slug": "three-squares-vii", "name": "three squares vii", "title": "Three Squares VII", "date": "2023-01-07", "statement": "Three squares. What’s the shaded area?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-squares-vii.lgf" }, { "slug": "subdivided-semi-circle", "name": "subdivided semi-circle", "title": "Subdivided Semi-Circle", "date": "2022-10-26", "statement": "The dots around the circumference of this semicircle are equally spaced. What fraction is shaded?", "categories": [ "Measures" ], "techniques": [], "drawing": "subdivided-semi-circle.lgf" }, { "slug": "three-squares-vi", "name": "three squares vi", "title": "Three Squares VI", "date": "2022-10-24", "statement": "The blue and green shaded regions created by these three squares have the same area. What’s the angle?", "categories": [ "Measures" ], "techniques": [], "drawing": "three-squares-vi.lgf", "live": true }, { "slug": "four-squares-and-a-triangle-ii", "name": "four squares and a triangle ii", "title": "Four Squares and a Triangle II", "date": "2022-08-26", "statement": "The triangle’s area is 4. What’s the total area of the four squares?", "categories": [ "Shapes" ], "techniques": [], "drawing": "four-squares-and-a-triangle-ii.lgf", "live": true }, { "slug": "five-equilateral-triangles-ii", "name": "five equilateral triangles ii", "title": "Five Equilateral Triangles II", "date": "2022-08-23", "statement": "The five triangles are equilateral. What’s the angle?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "five-equilateral-triangles-ii.lgf", "live": true }, { "slug": "three-semi-circles-in-a-rectangle", "name": "three semi-circles in a rectangle", "title": "Three Semi-Circles in a Rectangle", "date": "2022-08-19", "statement": "Is more of this rectangle red or blue?", "categories": [ "Measures" ], "techniques": [], "drawing": "three-semi-circles-in-a-rectangle.lgf" }, { "slug": "a-circle-in-a-rectangle", "name": "a circle in a rectangle", "title": "A Circle in a Rectangle", "date": "2022-08-17", "statement": "What’s the area of this rectangle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "a-circle-in-a-rectangle.lgf" }, { "slug": "two-squares-iii", "name": "two squares iii", "title": "Two Squares III", "date": "2022-08-16", "statement": "Two squares. What’s the missing area?", "categories": [ "Measures" ], "techniques": [], "drawing": "two-squares-iii.lgf" }, { "slug": "six-rectangles", "name": "six rectangles", "title": "Six Rectangles", "date": "2022-04-19", "statement": "6 congruent rectangles. What’s the angle?", "categories": [ "Shapes" ], "techniques": [], "drawing": "six-rectangles.lgf" }, { "slug": "four-houses-in-a-semi-circle", "name": "four houses in a semi-circle", "title": "Four Houses in a Semi-Circle", "date": "2022-04-14", "statement": "These houses are made from squares and equilateral triangles. What’s their total area?", "categories": [ "Measures" ], "techniques": [], "drawing": "four-houses-in-a-semi-circle.lgf" }, { "slug": "two-triangles-in-a-square", "name": "two triangles in a square", "title": "Two Triangles in a Square", "date": "2022-04-12", "statement": "The outer shape is a square. What’s the missing angle?", "categories": [ "Shapes" ], "techniques": [], "drawing": "two-triangles-in-a-square.lgf" }, { "slug": "subdivided-hexagon-iii", "name": "subdivided hexagon iii", "title": "Subdivided Hexagon III", "date": "2022-04-04", "statement": "What’s the total area of this regular hexagon?", "categories": [ "Shapes", "Algebra" ], "techniques": [], "drawing": "subdivided-hexagon-iii.lgf" }, { "slug": "three-squares-and-two-triangles", "name": "three squares and two triangles", "title": "Three Squares and Two Triangles", "date": "2022-03-16", "statement": "The two coloured triangles each have area 9. What’s the total area of the three squares?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-squares-and-two-triangles.lgf" }, { "slug": "a-quarter-circle-and-a-semi-circle-in-a-triangle", "name": "a quarter circle and a semi-circle in a triangle", "title": "A Quarter Circle and a Semi-Circle in a Triangle", "date": "2022-02-22", "statement": "What’s the area of the quarter circle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "a-quarter-circle-and-a-semi-circle-in-a-triangle.lgf" }, { "slug": "four-squares-and-a-triangle", "name": "four squares and a triangle", "title": "Four Squares and a Triangle", "date": "2022-02-20", "statement": "Four squares. What fraction of the total area does the yellow triangle cover?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "four-squares-and-a-triangle.lgf" }, { "slug": "two-equilateral-triangles-iii", "name": "two equilateral triangles iii", "title": "Two Equilateral Triangles III", "date": "2022-02-19", "statement": "Two equilateral triangles. What’s the angle?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "two-equilateral-triangles-iii.lgf", "live": true }, { "slug": "two-squares-ii", "name": "two squares ii", "title": "Two Squares II", "date": "2022-02-18", "statement": "Two squares. What’s the shaded area?", "categories": [ "Shapes", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "two-squares-ii.lgf", "live": true }, { "slug": "three-squares-and-a-triangle", "name": "three squares and a triangle", "title": "Three Squares and a Triangle", "date": "2022-02-17", "statement": "Each square has area 4. What’s the area of the pink right-angled triangle?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-squares-and-a-triangle.lgf" }, { "slug": "two-quarter-circles", "name": "two quarter circles", "title": "Two Quarter Circles", "date": "2022-02-16", "statement": "Two quarter circles. What’s the angle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-quarter-circles.lgf", "live": true }, { "slug": "a-square-and-a-triangle", "name": "a square and a triangle", "title": "A Square and a Triangle", "date": "2022-02-14", "statement": "The square has area 36. What’s the area of the right-angled triangle?", "categories": [ "Transformations and Symmetry", "Trigonometry" ], "techniques": [ "similarity" ], "drawing": "a-square-and-a-triangle.lgf" }, { "slug": "a-square-in-a-square", "name": "a square in a square", "title": "A Square in a Square", "date": "2021-12-20", "statement": "The shaded square covers half the larger square. What’s the angle?", "categories": [ "Shapes", "Trigonometry" ], "techniques": [], "drawing": "a-square-in-a-square.lgf" }, { "slug": "two-rectangles", "name": "two rectangles", "title": "Two Rectangles", "date": "2021-11-10", "statement": "How would you find the angle between the diagonals of these two rectangles?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "two-rectangles.lgf" }, { "slug": "subdivided-triangle-iii", "name": "subdivided triangle iii", "title": "Subdivided Triangle III", "date": "2021-10-23", "statement": "This isosceles triangle has been split into four smaller ones. What’s the missing angle?", "categories": [ "Shapes" ], "techniques": [], "drawing": "subdivided-triangle-iii.lgf" }, { "slug": "three-squares-v", "name": "three squares v", "title": "Three Squares V", "date": "2021-09-04", "statement": "Three squares. What’s the angle?", "categories": [ "Circle Theorems", "Other Techniques" ], "techniques": [ "angle at the circumference is half that at the centre", "invariance principle" ], "drawing": "three-squares-v.lgf", "live": true }, { "slug": "two-semi-circles-in-an-equilateral-triangle", "name": "two semi-circles in an equilateral triangle", "title": "Two Semi-Circles In an Equilateral Triangle", "date": "2021-08-11", "statement": "Two semicircles inside an equilateral triangle. What’s the angle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-semi-circles-in-an-equilateral-triangle.lgf", "live": true }, { "slug": "three-regular-hexagons-iv", "name": "three regular hexagons iv", "title": "Three Regular Hexagons IV", "date": "2021-08-10", "statement": "Three regular hexagons. What’s the angle?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-regular-hexagons-iv.lgf", "live": true }, { "slug": "five-regular-polygons", "name": "five regular polygons", "title": "Five Regular Polygons", "date": "2021-08-08", "statement": "All five polygons are regular. The red square has area 12. What’s the area of the blue square?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "five-regular-polygons.lgf", "live": true }, { "slug": "three-squares-and-a-rectangle", "name": "three squares and a rectangle", "title": "Three Squares and a Rectangle", "date": "2021-07-30", "statement": "Three squares and a rectangle. What’s the shaded area?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "three-squares-and-a-rectangle.lgf", "live": true }, { "slug": "three-quarter-circles-ii", "name": "three quarter circles ii", "title": "Three Quarter Circles II", "date": "2021-07-29", "statement": "Three quarter circles. What’s the total shaded area?", "categories": [ "Measures", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "three-quarter-circles-ii.lgf", "live": true }, { "slug": "two-equilateral-triangles-ii", "name": "two equilateral triangles ii", "title": "Two Equilateral Triangles II", "date": "2021-07-28", "statement": "Both triangles are equilateral. What’s the angle?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "two-equilateral-triangles-ii.lgf", "live": true }, { "slug": "two-semi-circles-and-two-quarter-circles", "name": "two semi-circles and two quarter circles", "title": "Two Semi-Circles and Two Quarter Circles", "date": "2021-07-26", "statement": "This design is made from two semicircles and two quarter circles. Is more of it shaded yellow or blue?", "categories": [ "Measures", "Trigonometry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "two-semi-circles-and-two-quarter-circles.lgf", "live": true }, { "slug": "five-squares", "name": "five squares", "title": "Five Squares", "date": "2021-07-25", "statement": "Five squares. What’s the total shaded area?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "similarity" ], "drawing": "five-squares.lgf" }, { "slug": "five-rectangles-in-a-semi-circle", "name": "five rectangles in a semi-circle", "title": "Five Rectangles in a Semi-Circle", "date": "2021-07-23", "statement": "What’s the total area of these five congruent rectangles?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "five-rectangles-in-a-semi-circle.lgf", "live": true }, { "slug": "two-squares-and-an-equilateral-triangle-ii", "name": "two squares and an equilateral triangle ii", "title": "Two Squares and an Equilateral Triangle II", "date": "2021-07-18", "statement": "Two squares and an equilateral triangle. What’s the angle?", "categories": [ "Shapes", "Measures" ], "techniques": [], "drawing": "two-squares-and-an-equilateral-triangle-ii.lgf" }, { "slug": "two-rectangles-and-a-square-ii", "name": "two rectangles and a square ii", "title": "Two Rectangles and a Square II", "date": "2021-07-18", "page": false, "categories": [], "techniques": [], "drawing": "two-rectangles-and-a-square-ii.lgf", "statement": "6 equal squares in a semicircle or in a quarter circle. Which area is larger - pink or blue?" }, { "slug": "subdivided-hexagon-ii", "name": "subdivided hexagon ii", "title": "Subdivided Hexagon II", "date": "2021-07-15", "statement": "What fraction of this regular hexagon is shaded?", "categories": [ "Shapes" ], "techniques": [], "drawing": "subdivided-hexagon-ii.lgf" }, { "slug": "four-congruent-triangles", "name": "four congruent triangles", "title": "Four Congruent Triangles", "date": "2021-07-11", "statement": "These four congruent triangles are laid out along a straight line. What’s the angle?", "categories": [ "Transformations and Symmetry", "Trigonometry" ], "techniques": [], "drawing": "four-congruent-triangles.lgf", "live": true }, { "slug": "two-circles", "name": "two circles", "title": "Two Circles", "date": "2021-07-03", "statement": "What’s the angle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-circles.lgf", "live": true }, { "slug": "three-congruent-rectangles-v", "name": "three congruent rectangles v", "title": "Three Congruent Rectangles V", "date": "2021-05-23", "statement": "These three rectangles are congruent. What’s the angle?", "categories": [ "Shapes" ], "techniques": [], "drawing": "three-congruent-rectangles-v.lgf" }, { "slug": "two-rectangles-and-a-square", "name": "two rectangles and a square", "title": "Two Rectangles and a Square", "date": "2021-05-16", "statement": "The two purple rectangles are congruent. What fraction of the square is shaded?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "two-rectangles-and-a-square.lgf" }, { "slug": "three-squares-ii", "name": "three squares ii", "title": "Three Squares II", "date": "2021-05-02", "statement": "Three squares. What’s the angle?", "categories": [ "Shapes", "Circle Theorems" ], "techniques": [], "drawing": "three-squares-ii.lgf", "live": true }, { "slug": "two-overlapping-triangles-ii", "name": "two overlapping triangles ii", "title": "Two Overlapping Triangles II", "date": "2021-04-11", "statement": "The largest of these two equilateral triangles has area $8$. What’s the blue area?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "symmetry", "invariance principle" ], "drawing": "two-overlapping-triangles-ii.lgf", "live": true }, { "slug": "two-regular-hexagons-iii", "name": "two regular hexagons iii", "title": "Two Regular Hexagons III", "date": "2021-04-10", "statement": "Both hexagons are regular. What’s the angle?", "categories": [ "Shapes" ], "techniques": [], "drawing": "two-regular-hexagons-iii.lgf" }, { "slug": "isosceles-and-equilateral-triangles", "name": "isosceles and equilateral triangles", "title": "Isosceles and Equilateral Triangles", "date": "2021-04-10", "statement": "A blue equilateral triangle overlaps a pink isosceles triangle. What’s the angle?", "categories": [ "Shapes", "Circle Theorems" ], "techniques": [ "angle at the circumference is half that at the centre" ], "drawing": "isosceles-and-equilateral-triangles.lgf", "live": true }, { "slug": "two-concentric-circles", "name": "two concentric circles", "title": "Two Concentric Circles", "date": "2021-04-10", "statement": "These two circles have the same centre. What’s the shaded area?", "categories": [ "Measures", "Circle Theorems" ], "techniques": [ "Pythagoras", "intersecting chords theorem" ], "drawing": "two-concentric-circles.lgf", "live": true }, { "slug": "four-squares-and-a-quarter-circle", "name": "four squares and a quarter circle", "title": "Four Squares and a Quarter Circle", "date": "2021-04-09", "statement": "The radius of the quarter circle is $5$. What’s the total area of the four squares?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "four-squares-and-a-quarter-circle.lgf" }, { "slug": "hexagon-and-a-square", "name": "hexagon and a square", "title": "Hexagon and a Square", "date": "2021-04-06", "statement": "A regular hexagon and a square. What’s the angle?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "transformation", "invariance principle" ], "drawing": "hexagon-and-a-square.lgf", "live": true }, { "slug": "two-quarter-circles-in-a-rectangle", "name": "two quarter circles in a rectangle", "title": "Two Quarter Circles in a Rectangle", "date": "2021-04-05", "statement": "What’s the sum of these two angles?", "categories": [ "Shapes" ], "techniques": [], "drawing": "two-quarter-circles-in-a-rectangle.lgf", "live": true }, { "slug": "four-squares-in-a-semi-circle", "name": "four squares in a semi-circle", "title": "Four Squares in a Semi-Circle", "date": "2021-04-04", "statement": "Four squares inside a semicircle. What’s the semicircle’s area?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "four-squares-in-a-semi-circle.lgf", "live": true }, { "slug": "triangle-in-two-tilted-squares", "name": "triangle in two tilted squares", "title": "Triangle in Two Tilted Squares", "date": "2021-04-03", "statement": "Two squares. What’s the shaded area?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "transformation", "invariance principle" ], "drawing": "triangle-in-two-tilted-squares.lgf", "live": true }, { "slug": "quarter-circle-overlapping-a-circle", "name": "quarter circle overlapping a circle", "title": "Quarter Circle Overlapping a Circle", "date": "2021-04-02", "statement": "What’s the sum of the two marked angles?", "categories": [ "Circle Theorems", "Other Techniques" ], "techniques": [ "angles in the same segment", "invariance principle" ], "drawing": "quarter-circle-overlapping-a-circle.lgf", "live": true }, { "slug": "five-equilateral-triangles", "name": "five equilateral triangles", "title": "Five Equilateral Triangles", "date": "2021-04-01", "statement": "The largest of these equilateral triangles has area $14$. What’s the total area of the other four?", "categories": [ "Measures", "Other Techniques" ], "techniques": [ "Pythagoras", "invariance principle" ], "drawing": "five-equilateral-triangles.lgf", "live": true }, { "slug": "four-equilateral-triangles-inside-a-hexagon", "name": "four equilateral triangles inside a hexagon", "title": "Four Equilateral Triangles Inside a Hexagon", "date": "2021-03-31", "statement": "Four equilateral triangles inside a regular hexagon. What fraction is shaded?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "symmetry" ], "drawing": "four-equilateral-triangles-inside-a-hexagon.lgf", "live": true }, { "slug": "two-quarter-circles-in-a-semi-circle-ii", "name": "two quarter circles in a semi-circle ii", "title": "Two Quarter Circles in a Semi-Circle II", "date": "2021-03-30", "statement": "The areas of the quarter circles are given. What’s the area of the semicircle?", "categories": [ "Transformations and Symmetry", "Circle Theorems" ], "techniques": [ "symmetry", "angle at the circumference is half that at the centre" ], "drawing": "two-quarter-circles-in-a-semi-circle-ii.lgf" }, { "slug": "three-squares-iii", "name": "three squares iii", "title": "Three Squares III", "date": "2021-03-29", "statement": "All three squares are the same size. What’s the angle?", "categories": [ "Shapes", "Circle Theorems", "Other Techniques" ], "techniques": [ "angle at the circumference is half that at the centre" ], "drawing": "three-squares-iii.lgf", "live": true }, { "slug": "four-squares-viii", "name": "four squares viii", "title": "Four Squares VIII", "date": "2021-03-28", "statement": "Four squares. What fraction is shaded?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "four-squares-viii.lgf" }, { "slug": "seven-quarter-circles-inside-a-semi-circle", "name": "seven quarter circles inside a semi-circle", "title": "Seven Quarter Circles Inside a Semi-Circle", "date": "2021-03-27", "statement": "What fraction of the semicircle do these quarter circles cover?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "seven-quarter-circles-inside-a-semi-circle.lgf" }, { "slug": "two-hexagons-and-a-triangle", "name": "two hexagons and a triangle", "title": "Two Hexagons and a Triangle", "date": "2021-03-26", "statement": "All three polygons here are regular. The area of the small hexagon is $5$. What’s the area of the large one?", "categories": [ "Circle Theorems" ], "techniques": [ "angle at the circumference is half that at the centre" ], "drawing": "two-hexagons-and-a-triangle.lgf", "live": true }, { "slug": "two-squares-inside-a-semi-circle", "name": "two squares inside a semi-circle", "title": "Two Squares Inside a Semi-Circle", "date": "2021-03-23", "statement": "Two squares inside a semicircle. What’s the angle?", "categories": [ "Circle Theorems" ], "techniques": [ "angle in a semi-circle" ], "drawing": "two-squares-inside-a-semi-circle.lgf", "live": true }, { "slug": "five-semi-circles", "name": "five semi-circles", "title": "Five Semi-Circles", "date": "2021-03-22", "statement": "A design made from $5$ semicircles. What’s the total shaded area?", "categories": [ "Measures", "Circle Theorems", "Other Techniques" ], "techniques": [ "Pythagoras", "parallelogram law", "invariance principle" ], "drawing": "five-semi-circles.lgf", "live": true }, { "slug": "four-squares-vii", "name": "four squares vii", "title": "Four Squares VII", "date": "2021-03-21", "statement": "The green area is $7$. What’s the total area of the four squares?", "categories": [ "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "four-squares-vii.lgf", "live": true }, { "slug": "four-parallel-semi-circles", "name": "four parallel semi-circles", "title": "Four Parallel Semi-Circles", "date": "2021-03-20", "statement": "The bases of all $4$ semicircles are parallel, and the largest one has diameter $8$. What’s the total shaded area?", "categories": [ "Circle Theorems", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "four-parallel-semi-circles.lgf", "live": true }, { "slug": "three-overlapping-hexagons", "name": "three overlapping hexagons", "title": "Three Overlapping Hexagons", "date": "2021-03-19", "statement": "Here are three overlapping regular hexagons. What’s the total red area?", "categories": [ "Shapes", "Measures" ], "techniques": [ "hexagon", "dissection" ], "drawing": "three-overlapping-hexagons.lgf" }, { "slug": "four-squares-vi", "name": "four squares vi", "title": "Four Squares VI", "date": "2021-03-18", "statement": "Four squares. What’s the total shaded area?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "four-squares-vi.lgf", "live": true }, { "slug": "two-squares-on-a-hexagon", "name": "two squares on a hexagon", "title": "Two Squares on a Hexagon", "date": "2021-03-17", "statement": "Two squares and a regular hexagon. What’s the angle?", "categories": [ "Shapes", "Transformations and Symmetry", "Circle Theorems", "Other Techniques" ], "techniques": [ "transformation", "invariance principle" ], "drawing": "two-squares-on-a-hexagon.lgf", "live": true }, { "slug": "semi-circles-in-a-rectangle", "name": "semi-circles in a rectangle", "title": "Semi-Circles in a Rectangle", "date": "2021-03-16", "statement": "The dots are equally spaced along the rectangle’s diagonal. What’s the total shaded area?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "semi-circles-in-a-rectangle.lgf" }, { "slug": "three-triangles-in-a-hexagon", "name": "three triangles in a hexagon", "title": "Three Triangles in a Hexagon", "date": "2021-03-15", "statement": "The two equilateral triangles are the same size. What’s the area of the regular hexagon?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "transformation", "invariance principle" ], "drawing": "three-triangles-in-a-hexagon.lgf", "live": true }, { "slug": "striped-semi-circle", "name": "striped semi-circle", "title": "Striped Semi-Circle", "date": "2021-03-14", "statement": "The points on the circumference are equally spaced. What’s the total shaded area?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "striped-semi-circle.lgf" }, { "slug": "two-quarter-circles-and-a-semi-circle-ii", "name": "two quarter circles and a semi-circle ii", "title": "Two Quarter Circles and a Semi-Circle II", "date": "2021-03-13", "statement": "Two quarter circles and a semicircle. What’s the total shaded area?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-quarter-circles-and-a-semi-circle-ii.lgf", "live": true }, { "slug": "five-quarter-circles", "name": "five quarter circles", "title": "Five Quarter Circles", "date": "2021-03-12", "statement": "This design is made of $5$ quarter circles. Is more of it shaded pink or purple?", "categories": [ "Measures" ], "techniques": [], "drawing": "five-quarter-circles.lgf", "live": true }, { "slug": "subdivided-hexagon", "name": "subdivided hexagon", "title": "Subdivided Hexagon", "date": "2021-03-10", "statement": "What’s the missing area in this regular hexagon?", "categories": [ "Shapes" ], "techniques": [ "triangle" ], "drawing": "subdivided-hexagon.lgf" }, { "slug": "multiple-semi-circles-iii", "name": "multiple semi-circles iii", "title": "Multiple Semi-Circles III", "date": "2021-03-07", "statement": "The red diameter is $6$. What’s the total shaded area?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "multiple-semi-circles-iii.lgf", "live": true }, { "slug": "three-overlapping-semi-circles", "name": "three overlapping semi-circles", "title": "Three Overlapping Semi-Circles", "date": "2021-03-06", "statement": "What’s the total shaded area?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "three-overlapping-semi-circles.lgf" }, { "slug": "three-quarter-circles", "name": "three quarter circles", "title": "Three Quarter Circles", "date": "2021-03-02", "statement": "Two of these quarter circles are the same size. What’s the angle?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-quarter-circles.lgf" }, { "slug": "two-squares-on-a-diameter-of-a-circle", "name": "two squares on a diameter of a circle", "title": "Two Squares on a Diameter of a Circle", "date": "2021-03-01", "page": false, "categories": [], "techniques": [], "drawing": "two-squares-on-a-diameter-of-a-circle.lgf", "live": true }, { "slug": "a-hexagon-and-a-nonagon", "name": "a hexagon and a nonagon", "title": "A Hexagon and a Nonagon", "date": "2021-02-28", "statement": "Two regular polygons. What’s the perimeter of the shaded region?", "categories": [ "Shapes" ], "techniques": [], "drawing": "a-hexagon-and-a-nonagon.lgf" }, { "slug": "four-quarter-circles-in-a-circle", "name": "four quarter circles in a circle", "title": "Four Quarter Circles in a Circle", "date": "2021-02-27", "statement": "What fraction of the circle do these four quarter circles cover?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "four-quarter-circles-in-a-circle.lgf", "live": true }, { "slug": "three-regular-hexagons-iii", "name": "three regular hexagons iii", "title": "Three Regular Hexagons III", "date": "2021-02-26", "statement": "Three regular hexagons. What fraction of the large hexagon is shaded?", "categories": [ "Shapes", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "three-regular-hexagons-iii.lgf", "live": true }, { "slug": "two-squares-overlapping-a-square-ii", "name": "two squares overlapping a square ii", "title": "Two Squares Overlapping a Square II", "date": "2021-02-23", "statement": "Three squares. What’s the green area?", "categories": [ "Transformations and Symmetry", "Circle Theorems" ], "techniques": [ "similarity", "angle at the circumference is half that at the centre" ], "drawing": "two-squares-overlapping-a-square-ii.lgf" }, { "slug": "three-congruent-triangles-ii", "name": "three congruent triangles ii", "title": "Three Congruent Triangles II", "date": "2021-02-21", "statement": "These triangles are congruent. What’s the angle?", "categories": [ "Shapes" ], "techniques": [], "drawing": "three-congruent-triangles-ii.lgf", "live": true }, { "slug": "two-triangles-overlapping-a-quarter-circle", "name": "two triangles overlapping a quarter circle", "title": "Two Triangles Overlapping a Quarter Circle", "date": "2021-02-20", "statement": "Both triangles are equilateral. What’s the area of the quarter circle?", "categories": [ "Circle Theorems", "Other Techniques" ], "techniques": [ "angle at the circumference is half that at the centre", "invariance principle" ], "drawing": "two-triangles-overlapping-a-quarter-circle.lgf", "live": true }, { "slug": "three-congruent-rectangles-iv", "name": "three congruent rectangles iv", "title": "Three Congruent Rectangles IV", "date": "2021-02-19", "statement": "Three congruent rectangles. What’s the angle?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "symmetry" ], "drawing": "three-congruent-rectangles-iv.lgf", "live": true }, { "slug": "three-congruent-triangles-in-a-semi-circle", "name": "three congruent triangles in a semi-circle", "title": "Three Congruent Triangles in a Semi-Circle", "date": "2021-02-18", "statement": "The three triangles are congruent. What’s the area of the semicircle?", "categories": [ "Shapes" ], "techniques": [ "circle" ], "drawing": "three-congruent-triangles-in-a-semi-circle.lgf", "live": true }, { "slug": "triangle-over-a-circle", "name": "triangle over a circle", "title": "Triangle Over a Circle", "date": "2021-02-17", "statement": "The triangle is equilateral. What’s the area of the circle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "triangle-over-a-circle.lgf", "live": true }, { "slug": "multiple-semi-circles-iv", "name": "multiple semi-circles iv", "title": "Multiple Semi-Circles IV", "date": "2021-02-16", "statement": "The three smallest semicircles are the same size. The area of the red semicircle is $10$. What’s the total yellow area?", "categories": [ "Measures" ], "techniques": [], "drawing": "multiple-semi-circles-iv.lgf" }, { "slug": "four-squares-v", "name": "four squares v", "title": "Four Squares V", "date": "2021-02-15", "statement": "A design made from four squares. Is more of it shaded pink or purple?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "four-squares-v.lgf", "live": true }, { "slug": "two-squares-overlapping-a-square", "name": "two squares overlapping a square", "title": "Two Squares Overlapping a Square", "date": "2021-02-14", "statement": "Three squares. The blue ones each have area 18. What’s the sum of the red lengths?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "congruent" ], "drawing": "two-squares-overlapping-a-square.lgf", "live": true }, { "slug": "zig-zag-inside-a-square", "name": "zig-zag inside a square", "title": "Zig-zag Inside a Square", "date": "2021-02-13", "statement": "What fraction of the square is shaded?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "zig-zag-inside-a-square.lgf" }, { "slug": "two-semi-circles-in-a-semi-circle", "name": "two semi-circles in a semi-circle", "title": "Two Semi-Circles in a Semi-Circle", "date": "2021-02-11", "statement": "What’s the area of the large semicircle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-semi-circles-in-a-semi-circle.lgf" }, { "slug": "six-triangles-in-a-hexagon", "name": "six triangles in a hexagon", "title": "Six Triangles in a Hexagon", "date": "2021-02-09", "statement": "What fraction of this regular hexagon do the equilateral triangles cover?", "categories": [ "Measures" ], "techniques": [ "area" ], "drawing": "six-triangles-in-a-hexagon.lgf" }, { "slug": "two-overlapping-triangles", "name": "two overlapping triangles", "title": "Two Overlapping Triangles", "date": "2021-02-07", "statement": "Two equilateral triangles. What’s the angle?", "categories": [ "Transformations and Symmetry", "Circle Theorems", "Other Techniques" ], "techniques": [ "similarity", "transformation", "invariance principle" ], "drawing": "two-overlapping-triangles.lgf", "live": true }, { "slug": "four-squares-inside-a-rectangle", "name": "four squares inside a rectangle", "title": "Four Squares Inside a Rectangle", "date": "2021-01-31", "statement": "Four squares inside a rectangle. What’s the angle?", "categories": [ "Shapes", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "four-squares-inside-a-rectangle.lgf", "live": true }, { "slug": "two-triangles-in-a-circle-and-semi-circle", "name": "two triangles in a circle and semi-circle", "title": "Two Triangles in a Circle and Semi-Circle", "date": "2021-01-30", "statement": "Which of the shaded triangles has the largest area?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-triangles-in-a-circle-and-semi-circle.lgf", "live": true }, { "slug": "triangle-in-a-rectangle", "name": "triangle in a rectangle", "title": "Triangle in a Rectangle", "date": "2021-01-29", "statement": "The three marked angles are equal. What fraction of the rectangle is shaded?", "categories": [ "Shapes", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "triangle-in-a-rectangle.lgf", "live": true }, { "slug": "multiple-semi-circles-ii", "name": "multiple semi-circles ii", "title": "Multiple Semi-Circles II", "date": "2021-01-27", "statement": "Is more of this design red or yellow?", "categories": [ "Shapes" ], "techniques": [ "lune" ], "drawing": "multiple-semi-circles-ii.lgf", "live": true }, { "slug": "square-overlapping-a-square-and-a-rectangle", "name": "square overlapping a square and a rectangle", "title": "Square Overlapping a Square and a Rectangle", "date": "2021-01-24", "statement": "The area of the largest square is $25$. What’s the combined area of the smaller square and rectangle?", "categories": [ "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "square-overlapping-a-square-and-a-rectangle.lgf", "live": true }, { "slug": "chord-splitting-a-square-in-half", "name": "chord splitting a square in half", "title": "Chord Splitting a Square in Half", "date": "2021-01-23", "statement": "A chord, of length $6$, splits the square in half. What’s the area of the semicircle?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "chord-splitting-a-square-in-half.lgf", "live": true }, { "slug": "rectangle-tilted-over-a-square", "name": "rectangle tilted over a square", "title": "Rectangle Tilted Over a Square", "date": "2021-01-16", "statement": "An orange rectangle and a black square. What’s the shaded area?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "similarity", "invariance principle" ], "drawing": "rectangle-tilted-over-a-square.lgf", "live": true }, { "slug": "multiple-angles", "name": "multiple angles", "title": "Multiple Angles", "date": "2021-01-10", "statement": "What’s the angle?", "categories": [ "Shapes", "Circle Theorems" ], "techniques": [], "drawing": "multiple-angles.lgf" }, { "slug": "three-circles-and-two-semi-circles-in-a-circle", "name": "three circles and two semi-circles in a circle", "title": "Three Circles and Two Semi-Circles in a Circle", "date": "2021-01-09", "statement": "The three small circles are the same size. What fraction of the large circle is shaded?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "three-circles-and-two-semi-circles-in-a-circle.lgf" }, { "slug": "four-triangles-in-a-square", "name": "four triangles in a square", "title": "Four Triangles in a Square", "date": "2020-12-31", "statement": "Four white equilateral triangles meet in the centre of this square. What’s the ratio of yellow to green in this design?", "categories": [ "Shapes" ], "techniques": [], "drawing": "four-triangles-in-a-square.lgf" }, { "slug": "zig-zag-inside-a-rectangle", "name": "zig-zag inside a rectangle", "title": "Zig-zag Inside a Rectangle", "date": "2020-12-30", "statement": "Rectangles of the same colour are similar. What’s the sum of the three marked angles?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "zig-zag-inside-a-rectangle.lgf", "live": true }, { "slug": "five-squares-across-a-square", "name": "five squares across a square", "title": "Five Squares Across a Square", "date": "2020-12-23", "statement": "Five squares. What’s the total shaded area?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "five-squares-across-a-square.lgf" }, { "slug": "two-squares-and-a-semi-circle", "name": "two squares and a semi-circle", "title": "Two Squares and a Semi-Circle", "date": "2020-12-13", "statement": "What’s the total area of these two squares?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-squares-and-a-semi-circle.lgf" }, { "slug": "two-circles-in-a-square-ii", "name": "two circles in a square ii", "title": "Two Circles in a Square II", "date": "2020-10-31", "statement": "Two circles in a square. What’s the angle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-circles-in-a-square-ii.lgf", "live": true }, { "slug": "triangles-formed-from-rectangles", "name": "triangles formed from rectangles", "title": "Triangles Formed from Rectangles", "date": "2020-10-29", "statement": "The area of the yellow triangle is $15$. What’s the total orange area?", "categories": [ "Shapes" ], "techniques": [ "trapezium" ], "drawing": "triangles-formed-from-rectangles.lgf", "live": true }, { "slug": "three-triangles-in-a-circle-in-a-triangle", "name": "three triangles in a circle in a triangle", "title": "Three Triangles in a Circle in a Triangle", "date": "2020-10-24", "statement": "All four triangles are equilateral. What fraction of the largest triangle is shaded?", "categories": [ "Trigonometry" ], "techniques": [], "drawing": "three-triangles-in-a-circle-in-a-triangle.lgf", "live": true }, { "slug": "two-quarter-circles-in-a-semi-circle", "name": "two quarter circles in a semi-circle", "title": "Two Quarter Circles in a Semi-Circle", "date": "2020-08-31", "statement": "What fraction of the semicircle do these quarter circles cover?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-quarter-circles-in-a-semi-circle.lgf" }, { "slug": "circle-inside-a-triangle", "name": "circle inside a triangle", "title": "Circle Inside a Triangle", "date": "2020-08-28", "statement": "What’s the area of the circle?", "categories": [ "Measures" ], "techniques": [], "drawing": "circle-inside-a-triangle.lgf" }, { "slug": "similar-rectangles", "name": "similar rectangles", "title": "Similar Rectangles", "date": "2020-08-26", "statement": "All the coloured rectangles are similar. What fraction of the design is red?", "categories": [ "Algebra" ], "techniques": [], "drawing": "similar-rectangles.lgf" }, { "slug": "two-semi-circles-in-a-circle", "name": "two semi-circles in a circle", "title": "Two Semi-Circles in a Circle", "date": "2020-08-21", "statement": "The bases of the semicircles are parallel. What fraction of the circle is shaded?", "categories": [ "Transformations and Symmetry", "Circle Theorems", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "two-semi-circles-in-a-circle.lgf", "live": true }, { "slug": "semi-circle-and-quarter-circle-in-a-square", "name": "semi-circle and quarter circle in a square", "title": "Semi-Circle and Quarter Circle in a Square", "date": "2020-08-17", "statement": "A semicircle and quarter circle inside a square. How long is the black tangent line?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "semi-circle-and-quarter-circle-in-a-square.lgf" }, { "slug": "multiple-semi-circles-in-a-circle", "name": "multiple semi-circles in a circle", "title": "Multiple Semi-Circles in a Circle", "date": "2020-08-15", "statement": "The green area is double the yellow area. What fraction of the total is shaded?", "categories": [ "Shapes" ], "techniques": [ "circle" ], "drawing": "multiple-semi-circles-in-a-circle.lgf", "live": true }, { "slug": "four-squares-iv", "name": "four squares iv", "title": "Four Squares IV", "date": "2020-08-14", "statement": "Four squares. What’s the angle?", "categories": [ "Circle Theorems", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "four-squares-iv.lgf", "live": true }, { "slug": "triangle-over-two-rectangles", "name": "triangle over two rectangles", "title": "Triangle Over Two Rectangles", "date": "2020-08-07", "statement": "Each coloured region has area $12$. What’s the area of the upper triangle?", "categories": [ "Shapes", "Measures" ], "techniques": [ "triangle", "dissection" ], "drawing": "triangle-over-two-rectangles.lgf", "live": true }, { "slug": "subdivided-decagon", "name": "subdivided decagon", "title": "Subdivided Decagon", "date": "2020-07-30", "statement": "What fraction of this regular decagon is shaded?", "categories": [ "Shapes" ], "techniques": [ "triangle" ], "drawing": "subdivided-decagon.lgf" }, { "slug": "two-congruent-rectangles-and-a-semi-circle", "name": "two congruent rectangles and a semi-circle", "title": "Two Congruent Rectangles and a Semi-Circle", "date": "2020-07-29", "statement": "The two rectangles are congruent. What’s the angle?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "two-congruent-rectangles-and-a-semi-circle.lgf" }, { "slug": "a-rectangle-in-a-square", "name": "a rectangle in a square", "title": "A Rectangle in a Square", "date": "2020-07-26", "statement": "The blue rectangle covers half of the square’s area. What’s the angle?", "categories": [ "Circle Theorems", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "a-rectangle-in-a-square.lgf", "live": true }, { "slug": "two-half-squares-and-a-circle", "name": "two half-squares and a circle", "title": "Two Half-Squares and a Circle", "date": "2020-07-25", "statement": "Two half squares, and a circle of radius $1$. What’s the total shaded area?", "categories": [ "Circle Theorems", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "two-half-squares-and-a-circle.lgf", "live": true }, { "slug": "three-congruent-rectangles-iii", "name": "three congruent rectangles iii", "title": "Three Congruent Rectangles III", "date": "2020-07-23", "statement": "The three green rectangles are congruent. What fraction of the square do they cover?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-congruent-rectangles-iii.lgf" }, { "slug": "squares-and-a-semi-circle", "name": "Squares and a Semi-Circle", "title": "Squares and a Semi-Circle", "date": "2020-07-22", "statement": "Some squares and a semicircle. What’s the perimeter of the combined shape?", "categories": [ "Shapes" ], "techniques": [ "circle" ], "drawing": "squares-and-a-semi-circle.lgf" }, { "slug": "semi-circle-in-a-square-in-a-quarter-circle", "name": "semi-circle in a square in a quarter circle", "title": "Semi-Circle in a Square in a Quarter Circle", "date": "2020-07-19", "statement": "The orange area is $10$. What’s the blue area?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "semi-circle-in-a-square-in-a-quarter-circle.lgf" }, { "slug": "two-triangles-and-three-concentric-semi-circles", "name": "two triangles and three concentric semi-circles", "title": "Two Triangles and Three Concentric Semi-Circles", "date": "2020-07-18", "statement": "Two right-angled triangles and three concentric semicircles. What fraction is yellow?", "categories": [ "Shapes", "Transformations and Symmetry" ], "techniques": [ "equilateral triangle", "similarity" ], "drawing": "two-triangles-and-three-concentric-semi-circles.lgf" }, { "slug": "five-congruent-rectangles", "name": "five congruent rectangles", "title": "Five Congruent Rectangles", "date": "2020-07-15", "statement": "Five congruent rectangles. What’s the angle?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "congruent" ], "drawing": "five-congruent-rectangles.lgf" }, { "slug": "five-rectangles-tiling-a-square", "name": "five rectangles tiling a square", "title": "Five Rectangles Tiling a Square", "date": "2020-07-11", "statement": "A square is split into five rectangles with equal areas. What’s the area of the square?", "categories": [ "Shapes" ], "techniques": [ "rectangle" ], "drawing": "five-rectangles-tiling-a-square.lgf" }, { "slug": "rectangle-overlapping-a-circle", "name": "rectangle overlapping a circle", "title": "Rectangle Overlapping a Circle", "date": "2020-07-05", "statement": "The four marked angles are equal. If the rectangle’s width is $3$, what’s the area of the circle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "rectangle-overlapping-a-circle.lgf", "live": true }, { "slug": "swirling-semi-circles", "name": "swirling semi-circles", "title": "Swirling Semi-Circles", "date": "2020-06-14", "statement": "The largest and smallest semicircles are concentric. What’s the shaded area?", "categories": [ "Measures" ], "techniques": [], "drawing": "swirling-semi-circles.lgf", "live": true }, { "slug": "hexagon-in-a-quarter-circle", "name": "hexagon in a quarter circle", "title": "Hexagon in a Quarter Circle", "date": "2020-05-31", "statement": "The hexagon is regular. What’s the area of the quarter circle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "hexagon-in-a-quarter-circle.lgf" }, { "slug": "six-semi-circles-inside-a-hexagon", "name": "six semi-circles inside a hexagon", "title": "Six Semi-Circles Inside a Hexagon", "date": "2020-05-30", "statement": "Six equal semicircles (and a circle) sitting in a regular hexagon. What fraction of the outer circle is shaded?", "categories": [ "Shapes" ], "techniques": [ "hexagon" ], "drawing": "six-semi-circles-inside-a-hexagon.lgf" }, { "slug": "four-quarter-circles", "name": "four quarter circles", "title": "Four Quarter Circles", "date": "2020-05-29", "statement": "Four quarter circles. What fraction is shaded?", "categories": [ "Measures" ], "techniques": [], "drawing": "four-quarter-circles.lgf" }, { "slug": "two-overlapping-triangles-and-a-circle", "name": "two overlapping triangles and a circle", "title": "Two Overlapping Triangles and a Circle", "date": "2020-05-28", "statement": "What’s the sum of these three angles?", "categories": [ "Circle Theorems", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "two-overlapping-triangles-and-a-circle.lgf", "live": true }, { "slug": "two-squares-diagonally-inside-a-rectangle", "name": "two squares diagonally inside a rectangle", "title": "Two Squares Diagonally Inside a Rectangle", "date": "2020-05-26", "statement": "Two squares sit on the diagonal of the rectangle. The red sections of the diagonal are equal length. What fraction of the rectangle is shaded?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "similarity" ], "drawing": "two-squares-diagonally-inside-a-rectangle.lgf" }, { "slug": "two-circles-and-two-semi-circles", "name": "two circles and two semi-circles", "title": "Two Circles and Two Semi-Circles", "date": "2020-05-25", "statement": "The yellow area is $16$. What’s the total black area?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-circles-and-two-semi-circles.lgf", "live": true }, { "slug": "two-tilted-squares", "name": "two tilted squares", "title": "Two Tilted Squares", "date": "2020-05-23", "statement": "Two squares. What’s the total pink area?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "two-tilted-squares.lgf", "live": true }, { "slug": "a-circle-and-two-semi-circles-in-two-hexagons", "name": "a circle and two semi-circles in two hexagons", "title": "A Circle and Two Semi-Circles in Two Hexagons", "date": "2020-05-14", "statement": "A circle and two semicircles are trapped by two overlapping regular hexagons. What fraction of the total area is shaded?", "categories": [ "Shapes" ], "techniques": [], "drawing": "a-circle-and-two-semi-circles-in-two-hexagons.lgf" }, { "slug": "four-squares-overlapping-a-rectangle", "name": "four squares overlapping a rectangle", "title": "Four Squares Overlapping a Rectangle", "date": "2020-05-09", "statement": "Each square has area $1$. What’s the area of the large rectangle?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "tessellation" ], "drawing": "four-squares-overlapping-a-rectangle.lgf" }, { "slug": "two-semi-circles-and-a-triangle", "name": "two semi-circles and a triangle", "title": "Two Semi-Circles and a Triangle", "date": "2020-05-08", "statement": "Two semicircles and a right-angled triangle. What’s the total shaded area?", "categories": [], "techniques": [], "drawing": "two-semi-circles-and-a-triangle.lgf" }, { "slug": "a-square-and-a-hexagon", "name": "a square and a hexagon", "title": "A Square and a Hexagon", "date": "2020-05-05", "statement": "Two regular polygons. What’s the angle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "a-square-and-a-hexagon.lgf", "live": true }, { "slug": "five-circles-in-a-square", "name": "five circles in a square", "title": "Five Circles in a Square", "date": "2020-05-02", "statement": "Five circles in a square. The total red area is $24$. What’s the total orange area?", "categories": [ "Trigonometry" ], "techniques": [], "drawing": "five-circles-in-a-square.lgf" }, { "slug": "two-quarter-circles-in-a-rectangle-in-a-semi-circle", "name": "two quarter circles in a rectangle in a semi-circle", "title": "Two Quarter Circles in a Rectangle in a Semi-Circle", "date": "2020-04-30", "statement": "Two quarter circles in a semicircle. What fraction is shaded?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "two-quarter-circles-in-a-rectangle-in-a-semi-circle.lgf" }, { "slug": "four-squares-iii", "name": "four squares iii", "title": "Four Squares III", "date": "2020-04-28", "statement": "Four squares. The blue area is $2$. What’s the green area?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "transformation", "invariance principle" ], "drawing": "four-squares-iii.lgf", "live": true }, { "slug": "four-squares-ii", "name": "four squares ii", "title": "Four Squares II", "date": "2020-04-26", "statement": "Four squares. What’s the shaded area?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "four-squares-ii.lgf" }, { "slug": "two-circles-inside-an-equilateral-triangle", "name": "two circles inside an equilateral triangle", "title": "Two Circles Inside an Equilateral Triangle", "date": "2020-04-25", "statement": "The triangle is equilateral. What’s the angle?", "categories": [ "Shapes", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "two-circles-inside-an-equilateral-triangle.lgf", "live": true }, { "slug": "three-congruent-rectangles-ii", "name": "three congruent rectangles ii", "title": "Three Congruent Rectangles II", "date": "2020-04-24", "statement": "The rectangles are congruent, each with area $9$. What’s the area of the triangle?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-congruent-rectangles-ii.lgf" }, { "slug": "four-congruent-squares-inside-a-larger-square", "name": "four congruent squares inside a larger square", "title": "Four Congruent Squares Inside a Larger Square", "date": "2020-04-23", "statement": "Four of the five squares are congruent. What’s the ratio of red to purple?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [], "drawing": "four-congruent-squares-inside-a-larger-square.lgf" }, { "slug": "two-semi-circles-and-an-equilateral-triangle", "name": "two semi-circles and an equilateral triangle", "title": "Two Semi-Circles and an Equilateral Triangle", "date": "2020-04-22", "statement": "The triangle is equilateral. What’s the total area of the two semicircles?", "categories": [ "Measures" ], "techniques": [], "drawing": "two-semi-circles-and-an-equilateral-triangle.lgf" }, { "slug": "two-quarter-circles-and-a-semi-circle", "name": "two quarter circles and a semi-circle", "title": "Two Quarter Circles and a Semi-Circle", "date": "2020-04-21", "statement": "Two quarter circles and a semicircle. What’s the shaded area?", "categories": [ "Shapes", "Other Techniques" ], "techniques": [ "circle", "invariance principle" ], "drawing": "two-quarter-circles-and-a-semi-circle.lgf", "live": true }, { "slug": "three-stacked-squares", "name": "three stacked squares", "title": "Three Stacked Squares", "date": "2020-04-19", "statement": "What’s the total area of these three squares?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "three-stacked-squares.lgf" }, { "slug": "two-circles-in-a-square", "name": "two circles in a square", "title": "Two Circles in a Square", "date": "2020-04-18", "statement": "What fraction of the square is shaded?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "two-circles-in-a-square.lgf" }, { "slug": "three-overlapping-rectangles-ii", "name": "three overlapping rectangles ii", "title": "Three Overlapping Rectangles II", "date": "2020-04-17", "statement": "The two small rectangles are congruent and each have area $12$. What’s the area of the large rectangle?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "similarity", "invariance principle" ], "drawing": "three-overlapping-rectangles-ii.lgf", "live": true }, { "slug": "semi-circle-splitting-a-triangle", "name": "semi-circle splitting a triangle", "title": "Semi-Circle Splitting a Triangle", "date": "2020-04-16", "statement": "The equilateral triangle has been split into two equal areas. What’s the area of the semicircle?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "semi-circle-splitting-a-triangle.lgf" }, { "slug": "two-semi-circles-diagonally-across-a-square", "name": "two semi-circles diagonally across a square", "title": "Two Semi-Circles Diagonally Across a Square", "date": "2020-04-15", "statement": "Two semicircles are placed on the diagonal of a square. What’s the total shaded area?", "categories": [ "Measures", "Other Techniques" ], "techniques": [ "Pythagoras", "invariance principle" ], "drawing": "two-semi-circles-diagonally-across-a-square.lgf", "live": true }, { "slug": "two-neighbouring-rectangles", "name": "two neighbouring rectangles", "title": "Two Neighbouring Rectangles", "date": "2020-04-13", "statement": "Both coloured regions have area $10$. What’s the total area of the two rectangles?", "categories": [ "Shapes" ], "techniques": [ "triangle" ], "drawing": "two-neighbouring-rectangles.lgf", "live": true }, { "slug": "two-overlapping-semi-circles", "name": "two overlapping semi-circles", "title": "Two Overlapping Semi-Circles", "date": "2020-04-12", "statement": "The larger semicircle has twice the area of the smaller one. What’s the angle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-overlapping-semi-circles.lgf", "live": true }, { "slug": "nested-semi-circles", "name": "nested semi-circles", "title": "Nested Semi-Circles", "date": "2020-04-11", "statement": "What fraction of the largest semicircle is shaded?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "nested-semi-circles.lgf" }, { "slug": "two-circles-in-a-triangle-ii", "name": "two circles in a triangle ii", "title": "Two Circles in a Triangle II", "date": "2020-04-10", "statement": "What fraction of this equilateral triangle is shaded?", "categories": [ "Shapes" ], "techniques": [ "equilateral triangle" ], "drawing": "two-circles-in-a-triangle-ii.lgf" }, { "slug": "tangential-hexagon-and-circle", "name": "tangential hexagon and circle", "title": "Tangential Hexagon and Circle", "date": "2020-04-09", "statement": "A unit circle is tangent to a regular hexagon. What’s the side length?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "tangential-hexagon-and-circle.lgf" }, { "slug": "three-overlapping-rectangles", "name": "three overlapping rectangles", "title": "Three Overlapping Rectangles", "date": "2020-04-08", "statement": "Which of these three rectangles has the largest area?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "tessellation" ], "drawing": "three-overlapping-rectangles.lgf", "live": true }, { "slug": "three-circles-forming-a-triangle", "name": "three circles forming a triangle", "title": "Three Circles Forming a Triangle", "date": "2020-04-07", "statement": "The circles have diameters $1$, $2$ and $3$. What’s the angle?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "three-circles-forming-a-triangle.lgf" }, { "slug": "four-squares-in-a-circle", "name": "four squares in a circle", "title": "Four Squares in a Circle", "date": "2020-04-06", "statement": "What’s the area of the circle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "four-squares-in-a-circle.lgf" }, { "slug": "three-equal-area-rectangles", "name": "three equal area rectangles", "title": "Three Equal Area Rectangles", "date": "2020-04-05", "statement": "All three of these rectangles have the same area. What is it?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "three-equal-area-rectangles.lgf" }, { "slug": "six-equal-area-rectangles", "name": "six equal area rectangles", "title": "Six Equal Area Rectangles", "date": "2020-04-04", "statement": "The six rectangles each have area $3$. What’s the total shaded area?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "six-equal-area-rectangles.lgf" }, { "slug": "angle-formed-by-three-squares", "name": "angle formed by three squares", "title": "Angle Formed by Three Squares", "date": "2020-04-02", "statement": "The squares are all the same size. What’s the angle?", "categories": [ "Trigonometry" ], "techniques": [ "trigonometry" ], "drawing": "angle-formed-by-three-squares.lgf" }, { "slug": "quadrilateral-splitting-a-semi-circle", "name": "quadrilateral splitting a semi-circle", "title": "Quadrilateral Splitting a Semi-Circle", "date": "2020-04-01", "statement": "In total, the blue arcs have the same length as the red. What’s the sum of these two angles?", "categories": [ "Circle Theorems", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "quadrilateral-splitting-a-semi-circle.lgf", "live": true }, { "slug": "two-regular-hexagons-ii", "name": "two regular hexagons ii", "title": "Two Regular Hexagons II", "date": "2020-03-28", "statement": "Both hexagons are regular. How long is the pink line?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "two-regular-hexagons-ii.lgf", "live": true }, { "slug": "three-squares-in-a-circle-ii", "name": "three squares in a circle ii", "title": "Three Squares in a Circle II", "date": "2020-03-21", "statement": "Three squares inside a circle. What’s the circle’s area?", "categories": [ "Algebra" ], "techniques": [], "drawing": "three-squares-in-a-circle-ii.lgf" }, { "slug": "rectangle-across-a-rectangle", "name": "rectangle across a rectangle", "title": "Rectangle Across a Rectangle", "date": "2020-03-16", "statement": "Here are two rectangles. $A B=5$, $A E=7$, $A F=1$. What’s the angle?", "categories": [ "Circle Theorems" ], "techniques": [ "angle at the circumference is half that at the centre" ], "drawing": "rectangle-across-a-rectangle.lgf" }, { "slug": "two-squares-and-an-equilateral-triangle", "name": "two squares and an equilateral triangle", "title": "Two Squares and an Equilateral Triangle", "date": "2020-03-14", "statement": "Two squares and an equilateral triangle. What’s the angle?", "categories": [ "Shapes" ], "techniques": [ "equation of a shape" ], "drawing": "two-squares-and-an-equilateral-triangle.lgf" }, { "slug": "quarter-circles-in-a-rectangle-in-a-circle", "name": "quarter circles in a rectangle in a circle", "title": "Quarter Circles in a Rectangle in a Circle", "date": "2020-03-07", "statement": "What fraction is shaded?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "quarter-circles-in-a-rectangle-in-a-circle.lgf" }, { "slug": "nested-isosceles-triangles", "name": "nested isosceles triangles", "title": "Nested Isosceles Triangles", "date": "2020-03-05", "statement": "Both the outer black triangle and inner pink triangle are isosceles, and the three coloured areas are equal. What’s the angle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "nested-isosceles-triangles.lgf" }, { "slug": "five-circles-in-a-rectangle-in-a-semi-circle", "name": "five circles in a rectangle in a semi-circle", "title": "Five Circles in a Rectangle in a Semi-Circle", "date": "2020-02-29", "statement": "Each of the small circles has area $1$. What’s the area of the semicircle?", "categories": [ "Measures" ], "techniques": [], "drawing": "five-circles-in-a-rectangle-in-a-semi-circle.lgf" }, { "slug": "two-semi-circles-inside-a-rectangle", "name": "two semi-circles inside a rectangle", "title": "Two Semi-Circles Inside a Rectangle", "date": "2020-02-23", "statement": "What fraction of the rectangle is shaded?", "categories": [ "Shapes" ], "techniques": [ "circle" ], "drawing": "two-semi-circles-inside-a-rectangle.lgf", "live": true }, { "slug": "two-squares-inside-an-equilateral-triangle", "name": "two squares inside an equilateral triangle", "title": "Two Squares Inside an Equilateral Triangle", "date": "2020-02-22", "statement": "Two squares inside an equilateral triangle. What’s the angle?", "categories": [ "Shapes" ], "techniques": [ "regular polygon" ], "drawing": "two-squares-inside-an-equilateral-triangle.lgf", "live": true }, { "slug": "tilted-rectangle-in-a-square", "name": "tilted rectangle in a square", "title": "Tilted Rectangle in a Square", "date": "2020-02-20", "statement": "What fraction of the square does this rectangle cover?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "symmetry" ], "drawing": "tilted-rectangle-in-a-square.lgf" }, { "slug": "circle-in-a-quarter-circle", "name": "circle in a quarter circle", "title": "Circle in a Quarter Circle", "date": "2020-02-18", "statement": "What's the total shaded area?", "categories": [ "Measures" ], "techniques": [], "drawing": "circle-in-a-quarter-circle.lgf", "live": true }, { "slug": "three-semi-circles", "name": "three semi-circles", "title": "Three Semi-Circles", "date": "2020-02-16", "statement": "The three coloured stripes are each the same width. If the smallest semicircle has area $5$, what's the area of the largest?", "categories": [ "Measures" ], "techniques": [], "drawing": "three-semi-circles.lgf" }, { "slug": "a-square-and-a-rectangle-overlapping", "name": "a square and a rectangle overlapping", "title": "A Square and a Rectangle Overlapping", "date": "2020-02-14", "statement": "$75\\%$ of the purple square is shaded. What percentage of the red rectangle is shaded?", "categories": [ "Measures" ], "techniques": [], "drawing": "a-square-and-a-rectangle-overlapping.lgf" }, { "slug": "three-circles-in-a-hexagon-in-a-circle", "name": "three circles in a hexagon in a circle", "title": "Three Circles in a Hexagon in a Circle", "date": "2020-02-10", "statement": "What fraction is shaded? The hexagon is regular.", "categories": [ "Shapes" ], "techniques": [ "hexagon" ], "drawing": "three-circles-in-a-hexagon-in-a-circle.lgf" }, { "slug": "three-circles", "name": "three circles", "title": "Three Circles", "date": "2020-02-08", "statement": "The small circles each have area $1$. What's the area of the large circle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "three-circles.lgf" }, { "slug": "three-squares-in-a-triangle", "name": "three squares in a triangle", "title": "Three Squares in a Triangle", "date": "2020-02-04", "statement": "The areas of the three squares are given. What's the area of the red triangle?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "similarity" ], "drawing": "three-squares-in-a-triangle.lgf" }, { "slug": "four-squares", "name": "four squares", "title": "Four Squares", "date": "2020-02-01", "statement": "$4$ squares. What's the shaded area?", "categories": [ "Measures", "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "dissection", "invariance principle" ], "drawing": "four-squares.lgf", "live": true }, { "slug": "arcs-in-a-semi-circle", "name": "arcs in a semi-circle", "title": "Arcs in a Semi-Circle", "date": "2020-01-30", "statement": "The two red arcs are the same length. What fraction of the semicircle is shaded?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "arcs-in-a-semi-circle.lgf", "live": true }, { "slug": "three-isoscelese-triangles-inside-a-triangle", "name": "three isoscelese triangles inside a triangle", "title": "Three Isoscelese Triangles Inside a Triangle", "date": "2020-01-23", "statement": "The three shaded triangles are isosceles. What's the missing angle?", "categories": [ "Shapes" ], "techniques": [], "drawing": "three-isoscelese-triangles-inside-a-triangle.lgf", "live": true }, { "slug": "square-and-rectangle-overlapping-in-a-semi-circle", "name": "square and rectangle overlapping in a semi-circle", "title": "Square and Rectangle Overlapping in a Semi-Circle", "date": "2020-01-16", "statement": "The square and rectangle intersect at the centre of the semicircle. What's the total yellow area?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "square-and-rectangle-overlapping-in-a-semi-circle.lgf" }, { "slug": "three-stacked-squares-and-a-fourth-square", "name": "three stacked squares and a fourth square", "title": "Three Stacked Squares and a Fourth Square", "date": "2020-01-12", "statement": "The three small squares each have area $4$. What's the total shaded area?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "congruent" ], "drawing": "three-stacked-squares-and-a-fourth-square.lgf", "live": true }, { "slug": "parallelogram-area", "name": "parallelogram area", "title": "Parallelogram Area", "date": "2020-01-07", "statement": "$a + b$ is a right angle. What's the area of the parallelogram?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "parallelogram-area.lgf" }, { "slug": "three-squares", "name": "three squares", "title": "Three Squares", "date": "2020-01-04", "statement": "The areas of the three squares are given. How long is the red line?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-squares.lgf" }, { "slug": "three-squares-iv", "name": "three squares iv", "title": "Three Squares IV", "date": "2020-01-01", "statement": "Three squares. The green square has area 16. What’s the area of the blue square?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "three-squares-iv.lgf", "live": true }, { "slug": "parallelogram-in-a-rectangle", "name": "parallelogram in a rectangle", "title": "Parallelogram in a Rectangle", "date": "2020-01-01", "statement": "What fraction is shaded?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "parallelogram-in-a-rectangle.lgf", "live": true }, { "slug": "three-circles-in-a-rectangle", "name": "three circles in a rectangle", "title": "Three Circles in a Rectangle", "date": "2019-12-31", "statement": "The circles each have radius $1$. What's the area of the rectangle?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "similarity" ], "drawing": "three-circles-in-a-rectangle.lgf" }, { "slug": "two-semi-circles-inside-a-semi-circle", "name": "two semi-circles inside a semi-circle", "title": "Two Semi-Circles Inside a Semi-Circle", "date": "2019-12-29", "statement": "The two shaded semicircles are the same size. What fraction of the larger semicircle do they cover?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-semi-circles-inside-a-semi-circle.lgf" }, { "slug": "two-squares", "name": "two squares", "title": "Two Squares", "date": "2019-12-28", "statement": "The red square has double the area of the yellow square. What's the angle?", "categories": [ "Shapes", "Circle Theorems" ], "techniques": [], "drawing": "two-squares.lgf" }, { "slug": "three-squares-and-an-equilateral-triangle", "name": "three squares and an equilateral triangle", "title": "Three Squares and an Equilateral Triangle", "date": "2019-12-26", "statement": "Three squares and an equilateral triangle. What's the area of the pink square?", "categories": [ "Shapes" ], "techniques": [], "drawing": "three-squares-and-an-equilateral-triangle.lgf" }, { "slug": "pentagram-in-a-circle", "name": "pentagram in a circle", "title": "Pentagram in a Circle", "date": "2019-12-24", "statement": "Angles of the same colour are the same size. What's the orange angle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "pentagram-in-a-circle.lgf" }, { "slug": "rectangle-quartered-by-semi-circles", "name": "rectangle quartered by semi-circles", "title": "Rectangle Quartered by Semi-Circles", "date": "2019-12-23", "statement": "What’s the area of the dark blue rectangle?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "rectangle-quartered-by-semi-circles.lgf", "live": true }, { "slug": "chord-dividing-a-triangle-into-two", "name": "chord dividing a triangle into two", "title": "Chord Dividing a Triangle into Two", "date": "2019-12-22", "statement": "A chord of length $2$ splits this right-angled triangle into two equal areas. What’s the area of the circle?", "categories": [], "techniques": [], "drawing": "chord-dividing-a-triangle-into-two.lgf", "live": true }, { "slug": "two-pentagons", "name": "two pentagons", "title": "Two Pentagons", "date": "2019-12-20", "statement": "Two regular pentagons. What's the angle?", "categories": [ "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "two-pentagons.lgf", "live": true }, { "slug": "two-circles-in-a-rectangle", "name": "two circles in a rectangle", "title": "Two Circles in a Rectangle", "date": "2019-12-17", "statement": "What's the angle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-circles-in-a-rectangle.lgf", "live": true }, { "slug": "angle-formed-by-three-rectangles", "name": "angle formed by three rectangles", "title": "Angle Formed by Three Rectangles", "date": "2019-12-14", "statement": "Three congruent rectangles. What’s the angle?", "categories": [ "Shapes" ], "techniques": [ "triangle" ], "drawing": "angle-formed-by-three-rectangles.lgf" }, { "slug": "two-rectangles-in-a-square", "name": "two rectangles in a square", "title": "Two Rectangles in a Square", "date": "2019-12-12", "statement": "The dots are equally spaced. What fraction of the square is shaded?", "categories": [ "Measures" ], "techniques": [ "area" ], "drawing": "two-rectangles-in-a-square.lgf" }, { "slug": "five-semi-circles-around-a-rectangle", "name": "five semi-circles around a rectangle", "title": "Five Semi-Circles Around a Rectangle", "date": "2019-12-11", "statement": "Three of these semicircles have area $36$. What's the total area of the other two?", "categories": [ "Measures" ], "techniques": [], "drawing": "five-semi-circles-around-a-rectangle.lgf" }, { "slug": "three-equal-angles-in-a-rectangle", "name": "three equal angles in a rectangle", "title": "Three Equal Angles in a Rectangle", "date": "2019-12-07", "statement": "The three angles are equal. What fraction of the rectangle is shaded?", "categories": [ "Shapes" ], "techniques": [], "drawing": "three-equal-angles-in-a-rectangle.lgf" }, { "slug": "a-square-a-circle-and-a-rectangle", "name": "a square, a circle, and a rectangle", "title": "A Square, A Circle, and a Rectangle", "date": "2019-12-04", "statement": "A square, a circle and a rectangle. What fraction of the total area is shaded?", "categories": [ "Measures" ], "techniques": [], "drawing": "a-square-a-circle-and-a-rectangle.lgf" }, { "slug": "three-right-angled-triangles", "name": "three right-angled triangles", "title": "Three Right-Angled Triangles", "date": "2019-11-30", "statement": "This pattern is made from three right angled triangles. The two red lengths are equal. What's the pink area?", "categories": [ "Shapes" ], "techniques": [], "drawing": "three-right-angled-triangles.lgf", "live": true }, { "slug": "two-rectangles-overlapping-a-square", "name": "two rectangles overlapping a square", "title": "Two Rectangles Overlapping a Square", "date": "2019-11-24", "statement": "The yellow square has double the area of the red rectangle. How tall is the green rectangle?", "categories": [ "Measures" ], "techniques": [], "drawing": "two-rectangles-overlapping-a-square.lgf", "live": true }, { "slug": "areas-in-a-crossed-trapezium", "name": "areas in a crossed trapezium", "title": "Areas in a Crossed Trapezium", "date": "2019-11-20", "statement": "The total blue area is equal to the purple area. What fraction of the trapezium is shaded?", "categories": [ "Shapes" ], "techniques": [ "trapezium" ], "drawing": "areas-in-a-crossed-trapezium.lgf", "live": true }, { "slug": "seven-hexagons", "name": "seven hexagons", "title": "Seven Hexagons", "date": "2019-11-18", "statement": "Seven regular hexagons. What fraction is shaded?", "categories": [ "Measures" ], "techniques": [], "drawing": "seven-hexagons.lgf" }, { "slug": "a-pattern-of-squares", "name": "a pattern of squares", "title": "A Pattern of Squares", "date": "2019-11-17", "statement": "A pattern of squares. All six coloured areas are equal. What fraction is shaded?", "categories": [ "Measures" ], "techniques": [], "drawing": "a-pattern-of-squares.lgf" }, { "slug": "three-hexagons-and-a-rectangle", "name": "three hexagons and a rectangle", "title": "Three Hexagons and a Rectangle", "date": "2019-11-15", "statement": "These hexagons are all regular. What fraction of the rectangle is shaded?", "categories": [ "Shapes" ], "techniques": [ "hexagon" ], "drawing": "three-hexagons-and-a-rectangle.lgf" }, { "slug": "six-circles-inside-a-circle-inside-a-square", "name": "six circles inside a circle inside a square", "title": "Six Circles Inside a Circle Inside a Square", "date": "2019-11-09", "statement": "The six small circles each have radius $1$. What's the total shaded area?", "categories": [ "Measures" ], "techniques": [], "drawing": "six-circles-inside-a-circle-inside-a-square.lgf" }, { "slug": "stacked-squares-inside-two-squares", "name": "stacked squares inside two squares", "title": "Stacked Squares Inside Two Squares", "date": "2019-11-07", "statement": "The purple squares are all the same size. I've arranged three of them symmetrically inside each of the two black squares. What's the missing length?", "categories": [ "Shapes" ], "techniques": [ "square" ], "drawing": "stacked-squares-inside-two-squares.lgf" }, { "slug": "three-squares-inside-a-triangle", "name": "three squares inside a triangle", "title": "Three Squares Inside a Triangle", "date": "2019-10-30", "statement": "Three squares inside a triangle. What's the sum of the two shaded areas?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-squares-inside-a-triangle.lgf", "live": true }, { "slug": "three-congruent-triangles", "name": "three congruent triangles", "title": "Three Congruent Triangles", "date": "2019-10-29", "statement": "Three congruent triangles. The black line bisects the top angle. What angle does this line make with the horizontal?", "categories": [ "Transformations and Symmetry", "Circle Theorems" ], "techniques": [], "drawing": "three-congruent-triangles.lgf" }, { "slug": "two-semi-circles-inside-a-semi-circle-ii", "name": "two semi-circles inside a semi-circle ii", "title": "Two Semi-Circles Inside a Semi-Circle II", "date": "2019-10-27", "statement": "What's the diameter of the largest semicircle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-semi-circles-inside-a-semi-circle-ii.lgf" }, { "slug": "multiple-semi-circles", "name": "multiple semi-circles", "title": "Multiple Semi-Circles", "date": "2019-10-25", "statement": "The three coloured regions have the same area. Altogether, what fraction of the shape do they cover?", "categories": [ "Shapes" ], "techniques": [ "circle" ], "drawing": "multiple-semi-circles.lgf" }, { "slug": "two-congruent-rectangles-in-a-square", "name": "two congruent rectangles in a square", "title": "Two Congruent Rectangles in a Square", "date": "2019-10-24", "statement": "Two congruent rectangles are packed into a square. What's the angle?", "categories": [ "Shapes", "Algebra" ], "techniques": [], "drawing": "two-congruent-rectangles-in-a-square.lgf" }, { "slug": "three-circles-in-a-rectangle-ii", "name": "three circles in a rectangle ii", "title": "Three Circles in a Rectangle II", "date": "2019-10-19", "statement": "I've stacked three right-angled triangles to make this rectangle. What's its area?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "similarity" ], "drawing": "three-circles-in-a-rectangle-ii.lgf" }, { "slug": "overlapping-triangles-in-a-circle", "name": "overlapping triangles in a circle", "title": "Overlapping Triangles in a Circle", "date": "2019-10-13", "statement": "The circle contains a square and two overlapping equilateral triangles. What's the area of this overlap?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "overlapping-triangles-in-a-circle.lgf" }, { "slug": "diagonal-in-a-square", "name": "diagonal in a square", "title": "Diagonal in a Square", "date": "2019-10-11", "statement": "The point lies on the diagonal of the square so that $a + b = c$. What's the angle?", "categories": [ "Shapes" ], "techniques": [ "equilateral triangle" ], "drawing": "diagonal-in-a-square.lgf" }, { "slug": "seven-circles", "name": "seven circles", "title": "Seven Circles", "date": "2019-10-05", "statement": "The centres of all seven circles are marked. The width of the shaded ring is $1$. What's its area?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "seven-circles.lgf" }, { "slug": "angles-in-two-hexagons", "name": "angles in two hexagons", "title": "Angles in Two Hexagons", "date": "2019-09-28", "statement": "Both hexagons are regular. What's the sum of these two angles?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "transformation", "invariance principle" ], "drawing": "angles-in-two-hexagons.lgf", "live": true }, { "slug": "three-overlapping-squares", "name": "three overlapping squares", "title": "Three Overlapping Squares", "date": "2019-09-19", "statement": "The side lengths of the two blue squares are given. What's the missing length?", "categories": [ "Circle Theorems", "Other Techniques" ], "techniques": [ "angle at the circumference is half that at the centre", "invariance principle" ], "drawing": "three-overlapping-squares.lgf", "live": true }, { "slug": "four-squares-and-a-semi-circle", "name": "four squares and a semi-circle", "title": "Four Squares and a Semi-Circle", "date": "2019-09-07", "statement": "If the biggest square has area $18$, what's the total area of all four squares?", "categories": [ "Circle Theorems" ], "techniques": [ "intersecting chords theorem" ], "drawing": "four-squares-and-a-semi-circle.lgf", "live": true }, { "slug": "two-overlapping-hexagons-and-a-rectangle", "name": "two overlapping hexagons and a rectangle", "title": "Two Overlapping Hexagons and a Rectangle", "date": "2019-09-02", "statement": "One corner of each regular hexagon lies on the diagonal of the rectangle. What fraction of the rectangle is shaded?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "two-overlapping-hexagons-and-a-rectangle.lgf" }, { "slug": "two-rectangles-of-equal-area", "name": "two rectangles of equal area", "title": "Two Rectangles of Equal Area", "date": "2019-08-31", "statement": "The pink and blue rectangles have the same area. What is it?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "two-rectangles-of-equal-area.lgf", "live": true }, { "slug": "three-squares-overlapping-a-semi-circle", "name": "three squares overlapping a semi-circle", "title": "Three Squares Overlapping a Semi-Circle", "date": "2019-08-29", "statement": "The two smaller squares each have area $4$. What's the area of the larger square?", "categories": [ "Circle Theorems" ], "techniques": [ "intersecting chords theorem" ], "drawing": "three-squares-overlapping-a-semi-circle.lgf", "live": true }, { "slug": "two-hexagons-and-a-square", "name": "two hexagons and a square", "title": "Two Hexagons and a Square", "date": "2019-08-28", "statement": "Two regular hexagons, and a square of side length $2$. What's the shaded area?", "categories": [ "Shapes" ], "techniques": [ "hexagon" ], "drawing": "two-hexagons-and-a-square.lgf" }, { "slug": "four-hexagons", "name": "four hexagons", "title": "Four Hexagons", "date": "2019-08-26", "statement": "Four regular hexagons. What's the pink area?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "transformation" ], "drawing": "four-hexagons.lgf", "live": true }, { "slug": "two-squares-in-a-semi-circle", "name": "two squares in a semi-circle", "title": "Two Squares in a Semi-Circle", "date": "2019-08-24", "statement": "What's the total area of these two squares?", "categories": [ "Circle Theorems", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "two-squares-in-a-semi-circle.lgf", "live": true }, { "slug": "three-squares-in-a-semi-circle", "name": "three squares in a semi-circle", "title": "Three Squares in a Semi-Circle", "date": "2019-08-23", "statement": "The two smallest squares each have area $6$. How long is the red line?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "three-squares-in-a-semi-circle.lgf" }, { "slug": "three-congruent-squares-overlapping-a-square", "name": "three congruent squares overlapping a square", "title": "Three Congruent Squares Overlapping a Square", "date": "2019-08-22", "statement": "The total area of the three identical squares is equal to the area of the large square. What's the angle?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-congruent-squares-overlapping-a-square.lgf" }, { "slug": "three-triangles-in-a-square", "name": "three triangles in a square", "title": "Three Triangles in a Square", "date": "2019-08-20", "statement": "Inside this square are three triangles of equal area. How long is the red line?", "categories": [ "Measures" ], "techniques": [], "drawing": "three-triangles-in-a-square.lgf" }, { "slug": "trisected-hexagon", "name": "trisected hexagon", "title": "Trisected Hexagon", "date": "2019-08-19", "statement": "This regular hexagon has been split into thirds. What’s the angle?", "categories": [ "Trigonometry" ], "techniques": [], "drawing": "trisected-hexagon.lgf" }, { "slug": "two-congruent-quadrilaterals-and-a-rectangle", "name": "two congruent quadrilaterals and a rectangle", "title": "Two Congruent Quadrilaterals and a Rectangle", "date": "2019-08-16", "statement": "Two congruent quadrilaterals and a rectangle. Which shaded region is larger, yellow or green?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "two-congruent-quadrilaterals-and-a-rectangle.lgf", "live": true }, { "slug": "semi-circle-in-a-square-ii", "name": "semi-circle in a square ii", "title": "Semi-Circle in a Square II", "date": "2019-08-14", "statement": "A semicircle in a square. What's the missing length?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "semi-circle-in-a-square-ii.lgf", "live": true }, { "slug": "circle-in-pentagon-in-semi-circle", "name": "circle in pentagon in semi-circle", "title": "Circle In Pentagon in Semi-Circle", "date": "2019-08-11", "statement": "A circle in a regular pentagon in a semicircle. What fraction of the semicircle is shaded?", "categories": [ "Shapes" ], "techniques": [ "pentagon" ], "drawing": "circle-in-pentagon-in-semi-circle.lgf" }, { "slug": "rectangles-in-concentric-rings", "name": "rectangles in concentric rings", "title": "Rectangles in Concentric Rings", "date": "2019-08-09", "statement": "Each rectangle is tangent to two of the concentric circles. If the inner blue right has area $4$, what's the purple area?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "rectangles-in-concentric-rings.lgf", "live": true }, { "slug": "three-regular-hexagons-ii", "name": "three regular hexagons ii", "title": "Three Regular Hexagons ii", "date": "2019-08-08", "statement": "The largest of these regular hexagons has area $9$. What's the shaded area?", "categories": [ "Shapes", "Other Techniques" ], "techniques": [], "drawing": "three-regular-hexagons-ii.lgf", "live": true }, { "slug": "one-rectangle-inside-another-with-semi-circles", "name": "one rectangle inside another with semi-circles", "title": "One Rectangle Inside Another With Semi-Circles", "date": "2019-08-05", "statement": "What fraction of the outer rectangle is shaded?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "one-rectangle-inside-another-with-semi-circles.lgf" }, { "slug": "two-rectangles-and-a-semi-circle", "name": "two rectangles and a semi-circle", "title": "Two Rectangles and a Semi-Circle", "date": "2019-08-03", "statement": "Two rectangles and a semicircle. What's the shaded area?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-rectangles-and-a-semi-circle.lgf" }, { "slug": "three-equilateral-triangles-and-a-semi-circle", "name": "three equilateral triangles and a semi-circle", "title": "Three Equilateral Triangles and a Semi-Circle", "date": "2019-08-02", "statement": "The three equilateral triangles have sides of length $12$. What's the area of the semicircle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "three-equilateral-triangles-and-a-semi-circle.lgf" }, { "slug": "three-circles-in-a-semi-circle", "name": "three circles in a semi-circle", "title": "Three Circles in a Semi-Circle", "date": "2019-08-01", "statement": "What fraction of the semicircle is not covered by these three identical circles?", "categories": [ "Shapes" ], "techniques": [ "hexagon" ], "drawing": "three-circles-in-a-semi-circle.lgf" }, { "slug": "upside-down-semi-circles-in-a-semi-circle", "name": "upside-down semi-circles in a semi-circle", "title": "Upside-Down Semi-Circles in a Semi-Circle", "date": "2019-07-30", "statement": "What proportion of each diagram is shaded? Give your answers as decimals. What comes next?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "upside-down-semi-circles-in-a-semi-circle.lgf" }, { "slug": "stacked-triangles", "name": "stacked triangles", "title": "Stacked Triangles", "date": "2019-07-29", "statement": "Three of the triangles in this stack are equilateral. Find the sum of the pink and green areas.", "categories": [ "Measures", "Trigonometry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "stacked-triangles.lgf", "live": true }, { "slug": "triangles-in-a-dodecagon", "name": "triangles in a dodecagon", "title": "Triangles in a Dodecagon", "date": "2019-07-27", "statement": "The difference between the orange and yellow areas is $2$. What's the total area of the regular dodecagon?", "categories": [ "Shapes" ], "techniques": [], "drawing": "triangles-in-a-dodecagon.lgf" }, { "slug": "angle-formed-by-two-squares-ii", "name": "angle formed by two squares ii", "title": "Angle Formed by Two Squares II", "date": "2019-07-26", "statement": "These squares are the same size. What’s the angle?", "categories": [ "Shapes", "Circle Theorems", "Other Techniques" ], "techniques": [ "isosceles triangle", "angle at the circumference is half that at the centre", "invariance principle" ], "drawing": "angle-formed-by-two-squares-ii.lgf", "live": true }, { "slug": "three-parallel-semi-circles", "name": "three parallel semi-circles", "title": "Three Parallel Semi-Circles", "date": "2019-07-24", "statement": "The bases of all three semicircles are horizontal. If the yellow region has area $6$, what's the total blue area?", "categories": [ "Measures" ], "techniques": [], "drawing": "three-parallel-semi-circles.lgf", "live": true }, { "slug": "semi-circle-in-a-right-angled-triangle", "name": "semi-circle in a right-angled triangle", "title": "Semi-Circle in a Right-Angled Triangle", "date": "2019-07-23", "statement": "A semi-circle sits in a right-angled triangle. What's the shaded area?", "categories": [ "Circle Theorems" ], "techniques": [ "angle between a radius and tangent" ], "drawing": "semi-circle-in-a-right-angled-triangle.lgf", "live": true }, { "slug": "three-congruent-squares-in-a-rectangle", "name": "three congruent squares in a rectangle", "title": "Three Congruent Squares in a Rectangle", "date": "2019-07-22", "statement": "What fraction of the rectangle is covered by these three identical squares?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "similarity" ], "drawing": "three-congruent-squares-in-a-rectangle.lgf", "live": true }, { "slug": "three-hexagons-in-a-trapezium", "name": "three hexagons in a trapezium", "title": "Three Hexagons in a Trapezium", "date": "2019-07-20", "statement": "The perimeters of the regular hexagons add up to $36$. How wide is the trapezium?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "three-hexagons-in-a-trapezium.lgf", "live": true }, { "slug": "regular-hexagon-and-rectangle", "name": "regular hexagon and rectangle", "title": "Regular Hexagon and Rectangle", "date": "2019-07-12", "statement": "Here’s a regular hexagon and a rectangle. What’s the angle?", "categories": [ "Circle Theorems", "Other Techniques" ], "techniques": [ "angle at the circumference is half that at the centre", "invariance principle" ], "drawing": "regular-hexagon-and-rectangle.lgf", "live": true }, { "slug": "stack-of-congruent-rectangles", "name": "stack of congruent rectangles", "title": "Stack of Congruent Rectangles", "date": "2019-06-28", "statement": "The height of this stack of congruent rectangles is $22$. What's the total shaded area?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "stack-of-congruent-rectangles.lgf" }, { "slug": "angles-in-a-circle", "name": "angles in a circle", "title": "Angles in a Circle", "date": "2019-06-27", "statement": "What's the sum of the three marked angles?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "angles-in-a-circle.lgf", "live": true }, { "slug": "striped-dodecagon", "name": "striped dodecagon", "title": "Striped Dodecagon", "date": "2019-06-24", "statement": "This dodecagon is regular. What's the total shaded area?", "categories": [ "Shapes" ], "techniques": [ "triangle" ], "drawing": "striped-dodecagon.lgf" }, { "slug": "two-squares-overlapping-a-third-square", "name": "two squares overlapping a third square", "title": "Two Squares Overlapping a Third Square", "date": "2019-06-15", "statement": "Two of these three squares have area $4$. What's the area of the blue triangle?", "categories": [ "Shapes" ], "techniques": [], "drawing": "two-squares-overlapping-a-third-square.lgf" }, { "slug": "three-squares-and-a-semi-circle", "name": "three squares and a semi-circle", "title": "Three Squares and a Semi-Circle", "date": "2019-06-07", "statement": "The smallest of these three squares has area $7$. What's the total shaded area?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "three-squares-and-a-semi-circle.lgf", "live": true }, { "slug": "three-congruent-rectangles", "name": "three congruent rectangles", "title": "Three Congruent Rectangles", "date": "2019-06-04", "statement": "Three congruent rectangles overlap. How long is the diagonal?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-congruent-rectangles.lgf" }, { "slug": "rectangle-circle-and-triangle", "name": "rectangle, circle, and triangle", "title": "Rectangle, Circle, and Triangle", "date": "2019-06-01", "statement": "A rectangle, a circle, and a $3-4-5$ triangle. What fraction of the rectangle is shaded?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "rectangle-circle-and-triangle.lgf" }, { "slug": "two-regular-hexagons", "name": "two regular hexagons", "title": "Two Regular Hexagons", "date": "2019-05-30", "statement": "How far apart are the corners of these two regular hexagons?", "categories": [ "Circle Theorems", "Other Techniques" ], "techniques": [ "angle at the circumference is half that at the centre", "invariance principle" ], "drawing": "two-regular-hexagons.lgf" }, { "slug": "angle-in-a-circle-and-semi-circle", "name": "angle in a circle and semi-circle", "title": "Angle in a Circle and Semi-Circle", "date": "2019-05-28", "statement": "What's the angle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "angle-in-a-circle-and-semi-circle.lgf", "live": true }, { "slug": "circle-and-two-squares", "name": "circle and two squares", "title": "Circle and Two Squares", "date": "2019-05-26", "statement": "A circle and two squares. What's the area of the circle?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "congruent" ], "drawing": "circle-and-two-squares.lgf", "live": true }, { "slug": "divided-hexagon", "name": "divided hexagon", "title": "Divided Hexagon", "date": "2019-05-25", "statement": "Each yellow region covers one third of the regular hexagon. What fraction is green?", "categories": [ "Shapes" ], "techniques": [], "drawing": "divided-hexagon.lgf" }, { "slug": "two-overlapping-squares", "name": "two overlapping squares", "title": "Two Overlapping Squares", "date": "2019-05-20", "statement": "Two overlapping squares. What's the shaded area?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "two-overlapping-squares.lgf", "live": true }, { "slug": "two-squares-in-a-triangle", "name": "two squares in a triangle", "title": "Two Squares in a Triangle", "date": "2019-05-19", "statement": "The perimeter of each square is $\\frac{1}{3}$ of the perimeter of the triangle. What fraction is shaded?", "categories": [ "Shapes" ], "techniques": [ "triangle" ], "drawing": "two-squares-in-a-triangle.lgf", "live": true }, { "slug": "a-semi-circle-and-quarter-circle-in-a-square", "name": "a semi-circle and quarter circle in a square", "title": "A Semi-Circle and Quarter Circle in a Square", "date": "2019-05-17", "statement": "What's the area of the square?", "categories": [ "Shapes" ], "techniques": [], "drawing": "a-semi-circle-and-quarter-circle-in-a-square.lgf" }, { "slug": "overlapping-triangle-and-hexagon", "name": "overlapping triangle and hexagon", "title": "Overlapping Triangle and Hexagon", "date": "2019-05-14", "statement": "One corner of the regular hexagon is on the midpoint of the triangle's base. What fraction of the total area is shaded?", "categories": [ "Shapes" ], "techniques": [], "drawing": "overlapping-triangle-and-hexagon.lgf" }, { "slug": "overlapping-triangle-and-rectangle", "name": "overlapping triangle and rectangle", "title": "Overlapping Triangle and Rectangle", "date": "2019-05-10", "statement": "The triangle and rectangle have the same area. What fraction of the total is shaded?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "similarity" ], "drawing": "overlapping-triangle-and-rectangle.lgf", "live": true }, { "slug": "divided-hexagon-ii", "name": "divided hexagon ii", "title": "Divided Hexagon II", "date": "2019-05-08", "statement": "What fraction of this regular hexagon is shaded?", "categories": [ "Shapes" ], "techniques": [], "drawing": "divided-hexagon-ii.lgf", "live": true }, { "slug": "semi-circle-between-two-quarter-circles", "name": "semi-circle between two quarter circles", "title": "Semi-Circle Between Two Quarter Circles", "date": "2019-05-06", "statement": "What's the angle?", "categories": [ "Measures" ], "techniques": [], "drawing": "semi-circle-between-two-quarter-circles.lgf" }, { "slug": "two-squares-and-two-equilateral-triangles-iii", "name": "two squares and two equilateral triangles iii", "title": "Two Squares and Two Equilateral Triangles III", "date": "2019-05-05", "statement": "If the small square has area $2$, what’s the shaded area?", "categories": [ "Measures" ], "techniques": [], "drawing": "two-squares-and-two-equilateral-triangles-iii.lgf" }, { "slug": "two-squares-and-two-equilateral-triangles-ii", "name": "two squares and two equilateral triangles ii", "title": "Two Squares and Two Equilateral Triangles II", "date": "2019-05-05", "statement": "Two squares and two equilateral triangles. If the area of the smaller square is $8$, what’s the shaded area?", "categories": [ "Measures" ], "techniques": [], "drawing": "two-squares-and-two-equilateral-triangles-ii.lgf" }, { "slug": "angles-in-two-circles", "name": "angles in two circles", "title": "Angles in Two Circles", "date": "2019-05-03", "statement": "What's the sum of the two marked angles?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "angles-in-two-circles.lgf", "live": true }, { "slug": "square-with-midpoints", "name": "square with midpoints", "title": "Square with Midpoints", "date": "2019-05-01", "statement": "Dots are midpoints. What fraction of the square is shaded?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "similarity" ], "drawing": "square-with-midpoints.lgf" }, { "slug": "angle-formed-by-two-squares", "name": "angle formed by two squares", "title": "Angle Formed by Two Squares", "date": "2019-04-28", "statement": "These squares are the same size. What’s the angle?", "categories": [ "Shapes" ], "techniques": [ "equilateral triangle" ], "drawing": "angle-formed-by-two-squares.lgf" }, { "slug": "two-circles-inside-two-polygons-inside-a-circle", "name": "two circles inside two polygons inside a circle", "title": "Two Circles Inside Two Polygons Inside a Circle", "date": "2019-04-26", "statement": "Two circles, inside two regular polygons, inside a large circle. What fraction is shaded?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-circles-inside-two-polygons-inside-a-circle.lgf" }, { "slug": "quartered-hexagon", "name": "quartered hexagon", "title": "Quartered Hexagon", "date": "2019-04-24", "statement": "Quarter of this regular hexagon is blue. What fraction is green?", "categories": [ "Shapes" ], "techniques": [], "drawing": "quartered-hexagon.lgf", "live": true }, { "slug": "two-semi-circles-in-a-square", "name": "two semi-circles in a square", "title": "Two Semi-Circles in a Square", "date": "2019-04-22", "statement": "The area of the square is $100$. What's the missing length?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-semi-circles-in-a-square.lgf", "live": true }, { "slug": "three-semi-circles-around-a-triangle", "name": "three semi-circles around a triangle", "title": "Three Semi-Circles Around a Triangle", "date": "2019-04-20", "statement": "What's the area of the red triangle?", "categories": [ "Shapes" ], "techniques": [ "triangle" ], "drawing": "three-semi-circles-around-a-triangle.lgf", "live": true }, { "slug": "two-overlapping-squares-ii", "name": "two overlapping squares ii", "title": "Two Overlapping Squares II", "date": "2019-04-18", "statement": "Half the total area of these overlapping squares is yellow. What fraction is orange?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "two-overlapping-squares-ii.lgf" }, { "slug": "two-rectangles-with-diagonals", "name": "two rectangles with diagonals", "title": "Two Rectangles with Diagonals", "date": "2019-04-17", "statement": "Two rectangles and their diagonals. What fraction of the total area is shaded?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "two-rectangles-with-diagonals.lgf" }, { "slug": "two-semi-circles-and-a-rectangle", "name": "two semi-circles and a rectangle", "title": "Two Semi-Circles and a Rectangle", "date": "2019-04-16", "statement": "A horizontal line of length $8$ joins these semicircles. What's the area of the rectangle?", "categories": [ "Circle Theorems" ], "techniques": [ "intersecting chords theorem" ], "drawing": "two-semi-circles-and-a-rectangle.lgf", "live": true }, { "slug": "semi-circle-on-a-hexagon", "name": "semi-circle on a hexagon", "title": "Semi-Circle on a Hexagon", "date": "2019-04-14", "statement": "One third of this regular hexagon is shaded. What's the area of the semicircle?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "semi-circle-on-a-hexagon.lgf" }, { "slug": "divided-square", "name": "divided square", "title": "Divided Square", "date": "2019-04-12", "statement": "The diagonal of the square has been divided into three sections of length $4$. What's the total shaded area?", "categories": [ "Shapes" ], "techniques": [], "drawing": "divided-square.lgf" }, { "slug": "three-adjacent-triangles", "name": "three adjacent triangles", "title": "Three Adjacent Triangles", "date": "2019-04-10", "statement": "Each equilateral triangle has been divided into pieces of equal area. What's the missing length?", "categories": [ "Shapes" ], "techniques": [ "triangle" ], "drawing": "three-adjacent-triangles.lgf" }, { "slug": "triangle-and-circle-inside-square", "name": "triangle and circle inside square", "title": "Triangle and Circle Inside Square", "date": "2019-04-07", "statement": "The equilateral triangle in the corner of this square is tangent to the circle where they touch. What's the diameter.", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "triangle-and-circle-inside-square.lgf" }, { "slug": "two-squares-on-a-triangle", "name": "two squares on a triangle", "title": "Two Squares on a Triangle", "date": "2019-04-04", "statement": "Two squares sit on the hypotenuse of a right-angled triangle. What's the angle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-squares-on-a-triangle.lgf", "live": true }, { "slug": "square-rectangle-and-two-semi-circles", "name": "square, rectangle, and two semi-circles", "title": "Square, Rectangle, and Two Semi-Circles", "date": "2019-04-03", "statement": "A square, a rectangle and two semicircles. Which shaded area is the larger?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "square-rectangle-and-two-semi-circles.lgf", "live": true }, { "slug": "three-triangles-and-a-rectangle-inside-a-circle", "name": "three triangles and a rectangle inside a circle", "title": "Three Triangles and a Rectangle Inside a Circle", "date": "2019-03-30", "statement": "Three equilateral triangles and a rectangle are stacked up inside this circle. What's the angle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "three-triangles-and-a-rectangle-inside-a-circle.lgf", "live": true }, { "slug": "triangle-inside-a-square", "name": "triangle inside a square", "title": "Triangle Inside a Square", "date": "2019-03-26", "statement": "The right-angled triangle covers $\\frac{1}{4}$ of the square. What fraction does the isosceles triangle cover?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "triangle-inside-a-square.lgf" }, { "slug": "triangle-inside-circle-and-triangle", "name": "triangle inside circle and triangle", "title": "Triangle Inside Circle and Triangle", "date": "2019-03-20", "statement": "One corner of the equilateral triangle is at the centre of the semicircle. What's the total area of the large black triangle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "triangle-inside-circle-and-triangle.lgf", "live": true }, { "slug": "circle-in-triangle-in-square", "name": "circle in triangle in square", "title": "Circle in Triangle in Square", "date": "2019-03-17", "statement": "A unit circle sits in an equilateral triangle inside a square. What's the total shaded area?", "categories": [ "Shapes" ], "techniques": [ "equilateral triangle" ], "drawing": "circle-in-triangle-in-square.lgf" }, { "slug": "quarter-circles-in-a-square-in-a-circle", "name": "quarter circles in a square in a circle", "title": "Quarter Circles in a Square in a Circle", "date": "2019-03-16", "statement": "The area where these two quarter circles overlap is $16$. What's the total shaded area?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "similarity" ], "drawing": "quarter-circles-in-a-square-in-a-circle.lgf" }, { "slug": "triangle-overlapping-a-hexagon", "name": "triangle overlapping a hexagon", "title": "Triangle Overlapping a Hexagon", "date": "2019-03-13", "statement": "If the area of the regular hexagon is $24$, what's the area of the equilateral triangle?", "categories": [ "Measures" ], "techniques": [], "drawing": "triangle-overlapping-a-hexagon.lgf" }, { "slug": "two-circles-in-a-triangle", "name": "two circles in a triangle", "title": "Two Circles in a Triangle", "date": "2019-03-10", "statement": "What's the area of this triangle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-circles-in-a-triangle.lgf" }, { "slug": "inverse-star-in-a-rectangle", "name": "inverse star in a rectangle", "title": "Inverse Star in a Rectangle", "date": "2019-03-07", "statement": "All four triangles are equilateral. What fraction of the rectangle do they cover?", "categories": [ "Shapes" ], "techniques": [ "equilateral triangle", "isosceles triangle" ], "drawing": "inverse-star-in-a-rectangle.lgf" }, { "slug": "three-overlapping-circles", "name": "three overlapping circles", "title": "Three Overlapping Circles", "date": "2019-03-03", "statement": "What's the total shaded area?", "categories": [ "Measures" ], "techniques": [], "drawing": "three-overlapping-circles.lgf" }, { "slug": "three-tilted-rectangles", "name": "three tilted rectangles", "title": "Three Tilted Rectangles", "date": "2019-03-01", "statement": "This design is made of three $2 \t\\times 1$ rectangles. What fraction of it is shaded?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-tilted-rectangles.lgf" }, { "slug": "overlapping-hexagons", "name": "overlapping hexagons", "title": "Overlapping Hexagons", "date": "2019-02-26", "statement": "Two regular hexagons overlap to create three equal areas. What's the perimeter of the design?", "categories": [ "Shapes" ], "techniques": [], "drawing": "overlapping-hexagons.lgf" }, { "slug": "square-overlapping-a-quarter-circle", "name": "square overlapping a quarter circle", "title": "Square Overlapping a Quarter Circle", "date": "2019-02-24", "statement": "The three coloured sections here have the same area. What's the total area of the square?", "categories": [ "Measures" ], "techniques": [], "drawing": "square-overlapping-a-quarter-circle.lgf" }, { "slug": "two-hexagons-in-a-rectangle", "name": "two hexagons in a rectangle", "title": "Two Hexagons in a Rectangle", "date": "2019-02-23", "statement": "Both the regular hexagons have area $6$. What's the total shaded area?", "categories": [ "Shapes" ], "techniques": [ "hexagon" ], "drawing": "two-hexagons-in-a-rectangle.lgf" }, { "slug": "semi-circle-in-a-circle", "name": "semi-circle in a circle", "title": "Semi-Circle in a Circle", "date": "2019-02-22", "statement": "What fraction of the circle is shaded?", "categories": [ "Circle Theorems" ], "techniques": [ "intersecting chords theorem" ], "drawing": "semi-circle-in-a-circle.lgf" }, { "slug": "two-triangles-overlapping-a-rectangle", "name": "two triangles overlapping a rectangle", "title": "Two Triangles Overlapping a Rectangle", "date": "2019-02-21", "statement": "What fraction of the rectangle is not covered by these two equilateral triangles?", "categories": [ "Shapes" ], "techniques": [ "equilateral triangle" ], "drawing": "two-triangles-overlapping-a-rectangle.lgf", "live": true }, { "slug": "square-on-an-octagon", "name": "square on an octagon", "title": "Square on an Octagon", "date": "2019-02-19", "statement": "Two of the square's corners lie on the regular octagon. What's the angle?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "square-on-an-octagon.lgf", "live": true }, { "slug": "circle-and-semi-circle-in-triangle", "name": "circle and semi-circle in triangle", "title": "Circle and Semi-Circle in Triangle", "date": "2019-02-18", "statement": "What's the area of the semicircle inside this equilateral triangle?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "circle-and-semi-circle-in-triangle.lgf" }, { "slug": "overlapping-triangles", "name": "overlapping triangles", "title": "Overlapping Triangles", "date": "2019-02-16", "statement": "When I place two $3-4-5$ triangles like this, what's the overlapping area?", "categories": [ "Shapes" ], "techniques": [ "rectangle" ], "drawing": "overlapping-triangles.lgf" }, { "slug": "tilted-rectangles", "name": "tilted rectangles", "title": "Tilted Rectangles", "date": "2019-02-13", "statement": "The two rectangles are congruent. What's the shaded area?", "categories": [ "Shapes" ], "techniques": [ "parallelogram" ], "drawing": "tilted-rectangles.lgf" }, { "slug": "triangle-in-semi-circle-with-square", "name": "triangle in semi-circle with square", "title": "Triangle in Semi-Circle with Square", "date": "2019-02-11", "statement": "The equilateral triangle sits in the centre of the semicircle. What's the area of the square?", "categories": [ "Measures" ], "techniques": [], "drawing": "triangle-in-semi-circle-with-square.lgf" }, { "slug": "circles-in-overlapping-triangles", "name": "circles in overlapping triangles", "title": "Circles in Overlapping Triangles", "date": "2019-02-07", "statement": "Two overlapping equilateral triangles each have an area of $100$. The three circles are the same size. What's the total area of the design?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "circles-in-overlapping-triangles.lgf" }, { "slug": "tilted-triangles", "name": "tilted triangles", "title": "Tilted Triangles", "date": "2019-02-02", "statement": "The two equilateral triangles are congruent. What's the angle?", "categories": [ "Circle Theorems" ], "techniques": [ "angle at the circumference is half that at the centre" ], "drawing": "tilted-triangles.lgf", "live": true }, { "slug": "two-quarter-circles-in-a-square", "name": "two quarter circles in a square", "title": "Two Quarter Circles in a Square", "date": "2019-01-28", "statement": "Two quarter circles inside a square. What fraction is shaded?", "categories": [ "Shapes" ], "techniques": [], "drawing": "two-quarter-circles-in-a-square.lgf" }, { "slug": "two-squares-and-a-rectangle-in-an-octagon", "name": "two squares and a rectangle in an octagon", "title": "Two Squares and a Rectangle in an Octagon", "date": "2019-01-26", "statement": "Inside this regular octagon sit two squares of area $8$. What's the area of the shaded rectangle?", "categories": [ "Shapes", "Measures" ], "techniques": [ "square", "Pythagoras" ], "drawing": "two-squares-and-a-rectangle-in-an-octagon.lgf" }, { "slug": "square-overlapping-a-circle", "name": "square overlapping a circle", "title": "Square Overlapping a Circle", "date": "2019-01-25", "statement": "A square, and a circle of radius $2$. What's the total shaded area?", "categories": [ "Circle Theorems" ], "techniques": [ "intersecting chords theorem" ], "drawing": "square-overlapping-a-circle.lgf" }, { "slug": "six-semi-circles-in-a-circle", "name": "six semi-circles in a circle", "title": "Six Semi-Circles in a Circle", "date": "2019-01-21", "statement": "A semicircle drawn on each side of a regular hexagon. What fraction of the outer circle is shaded?", "categories": [ "Shapes" ], "techniques": [ "hexagon" ], "drawing": "six-semi-circles-in-a-circle.lgf" }, { "slug": "rectangle-on-a-hexagon", "name": "rectangle on a hexagon", "title": "Rectangle on a Hexagon", "date": "2019-01-19", "statement": "The area of the regular hexagon is $30$. What's the area of the rectangle?", "categories": [ "Measures", "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "dissection", "transformation", "invariance principle" ], "drawing": "rectangle-on-a-hexagon.lgf", "live": true }, { "slug": "two-squares-on-a-circle", "name": "two squares on a circle", "title": "Two Squares on a Circle", "date": "2019-01-16", "statement": "The radius of the circle is $4$. What's the combined area of the two squares?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-squares-on-a-circle.lgf", "live": true }, { "slug": "pentagon-with-two-semi-circles", "name": "pentagon with two semi-circles", "title": "Pentagon with two Semi-Circles", "date": "2019-01-14", "statement": "The regular pentagon is tangent to both semicircles at the point where the three meet. What's the angle between the bases of the semicircles? What if I started with other regular polygons?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "pentagon-with-two-semi-circles.lgf", "live": true }, { "slug": "striped-hexagon", "name": "striped hexagon", "title": "Striped Hexagon", "date": "2019-01-13", "statement": "Is more of this regular hexagon red or blue? By how much?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "tessellation" ], "drawing": "striped-hexagon.lgf" }, { "slug": "circle-in-a-hexagon-in-a-semi-circle", "name": "circle in a hexagon in a semi-circle", "title": "Circle in a Hexagon in a Semi-Circle", "date": "2019-01-11", "statement": "The hexagon is regular. What fraction of the semicircle is shaded?", "categories": [ "Measures" ], "techniques": [], "drawing": "circle-in-a-hexagon-in-a-semi-circle.lgf" }, { "slug": "overlapping-rectangle-and-semi-circle", "name": "overlapping rectangle and semi-circle", "title": "Overlapping Rectangle and Semi-Circle", "date": "2019-01-05", "statement": "What's the area of the rectangle?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "overlapping-rectangle-and-semi-circle.lgf", "live": true }, { "slug": "two-rectangles-in-a-semi-circle", "name": "two rectangles in a semi-circle", "title": "Two Rectangles in a Semi-Circle", "date": "2018-12-31", "statement": "Two congruent rectangles sitting in a semicircle. What's the angle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-rectangles-in-a-semi-circle.lgf", "live": true }, { "slug": "divided-hexagon-iii", "name": "divided hexagon iii", "title": "Divided Hexagon III", "date": "2018-12-30", "statement": "The purple lines create two kites inside this regular hexagon. What's the missing area?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "divided-hexagon-iii.lgf" }, { "slug": "circles-around-a-triangle", "name": "circles around a triangle", "title": "Circles Around a Triangle", "date": "2018-12-16", "statement": "The diameters of these circles form a $3-4-5$ triangle. What's the total shaded area?", "categories": [ "Measures" ], "techniques": [], "drawing": "circles-around-a-triangle.lgf" }, { "slug": "rectangles-stacked-in-a-semi-circle", "name": "rectangles stacked in a semi-circle", "title": "Rectangles Stacked in a Semi-Circle", "date": "2018-12-12", "statement": "Three identical rectangles are stacked inside a semicircle. Find the total shaded area.", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "rectangles-stacked-in-a-semi-circle.lgf" }, { "slug": "two-circles-two-squares", "name": "two circles, two squares", "title": "Two Circles, Two Squares", "date": "2018-12-11", "statement": "Two circles, two squares. What's the shaded area?", "categories": [ "Shapes" ], "techniques": [ "square" ], "drawing": "two-circles-two-squares.lgf" }, { "slug": "subdivided-square", "name": "subdivided square", "title": "Subdivided Square", "date": "2018-12-05", "statement": "This pattern uses the corners of the square and midpoints of some of the sides. What fraction is yellow?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "subdivided-square.lgf" }, { "slug": "chords-dividing-a-triangle-into-five", "name": "chords dividing a triangle into five", "title": "Chords Dividing a Triangle into Five", "date": "2018-12-03", "statement": "A triangle is divided into five parts by chords of the circle. What’s the total area of the triangle?", "categories": [ "Circle Theorems" ], "techniques": [ "intersecting chords theorem" ], "drawing": "chords-dividing-a-triangle-into-five.lgf", "live": true }, { "slug": "three-rectangles-as-a-triangle", "name": "three rectangles as a triangle", "title": "Three Rectangles as a Triangle", "date": "2018-12-01", "statement": "These three overlapping rectangles are congruent, each with area $4$. The black dots mark the midpoints of the short sides. What total area is covered by this design?", "categories": [ "Shapes" ], "techniques": [], "drawing": "three-rectangles-as-a-triangle.lgf" }, { "slug": "partitioned-square", "name": "partitioned square", "title": "Partitioned Square", "date": "2018-11-28", "statement": "The four sections in this square have the same area. What's the missing length?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "partitioned-square.lgf" }, { "slug": "two-squares-overlapping-a-semi-circle", "name": "two squares overlapping a semi-circle", "title": "Two Squares Overlapping a Semi-Circle", "date": "2018-11-26", "statement": "Find the area of the semicircle. (Blue shapes are squares)", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "two-squares-overlapping-a-semi-circle.lgf", "live": true }, { "slug": "five-triangles-in-a-rectangle", "name": "five triangles in a rectangle", "title": "Five Triangles in a Rectangle", "date": "2018-11-25", "statement": "Five copies of the same triangle have been fitted into a rectangle. What fraction of it do they cover?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "five-triangles-in-a-rectangle.lgf" }, { "slug": "nested-circles-and-a-triangle", "name": "nested circles and a triangle", "title": "Nested Circles and a Triangle", "date": "2018-11-24", "statement": "What fraction is shaded? The triangle is equilateral.", "categories": [ "Shapes" ], "techniques": [ "equilateral triangle" ], "drawing": "nested-circles-and-a-triangle.lgf" }, { "slug": "square-in-a-triangle-in-a-square", "name": "square in a triangle in a square", "title": "Square in a Triangle in a Square", "date": "2018-11-23", "statement": "The sides of the two squares are parallel to each other. What's the ratio of the blue area to the yellow?", "categories": [ "Measures", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "square-in-a-triangle-in-a-square.lgf", "live": true }, { "slug": "quarter-circles-in-a-rectangle", "name": "quarter circles in a rectangle", "title": "Quarter Circles in a Rectangle", "date": "2018-11-22", "statement": "The black line is tangent to both quarter circles. What fraction of the rectangle is shaded?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "quarter-circles-in-a-rectangle.lgf" }, { "slug": "semi-circles-in-a-quarter-circle", "name": "semi-circles in a quarter circle", "title": "Semi-Circles in a Quarter Circle", "date": "2018-11-21", "statement": "What's the shaded area?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "similarity" ], "drawing": "semi-circles-in-a-quarter-circle.lgf" }, { "slug": "three-squares-on-a-line", "name": "three squares on a line", "title": "Three Squares on a Line", "date": "2018-11-19", "statement": "The areas of the three squares are given. What area is shaded?", "categories": [ "Shapes" ], "techniques": [ "square" ], "drawing": "three-squares-on-a-line.lgf" }, { "slug": "nested-circles-and-polygons", "name": "nested circles and polygons", "title": "Nested Circles and Polygons", "date": "2018-11-18", "statement": "Two circles, a rectangle and a regular hexagon, all neatly packed inside each other. What fraction of the outer circle is shaded?", "categories": [ "Measures" ], "techniques": [], "drawing": "nested-circles-and-polygons.lgf" }, { "slug": "semi-circle-and-tangents-in-a-square", "name": "semi-circle and tangents in a square", "title": "Semi-Circle and Tangents in a Square", "date": "2018-11-17", "statement": "The yellow lines are tangents to the semicircle. What fraction of the square is shaded?", "categories": [ "Measures", "Circle Theorems" ], "techniques": [ "Pythagoras" ], "drawing": "semi-circle-and-tangents-in-a-square.lgf" }, { "slug": "equilateral-triangle-in-a-hexagon", "name": "equilateral triangle in a hexagon", "title": "Equilateral Triangle in a Hexagon", "date": "2018-11-17", "statement": "What proportion of the hexagon is shaded?", "categories": [ "Shapes" ], "techniques": [], "drawing": "equilateral-triangle-in-a-hexagon.lgf" }, { "slug": "three-regular-hexagons", "name": "three regular hexagons", "title": "Three Regular Hexagons", "date": "2018-11-14", "statement": "Three regular hexagons. What fraction is shaded?", "categories": [ "Shapes" ], "techniques": [ "hexagon" ], "drawing": "three-regular-hexagons.lgf" }, { "slug": "triangles-in-a-semi-circle", "name": "triangles in a semi-circle", "title": "Triangles in a Semi-Circle", "date": "2018-11-13", "statement": "What's the area of the semicircle?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "similarity" ], "drawing": "triangles-in-a-semi-circle.lgf" }, { "slug": "equilateral-triangles-in-a-square", "name": "equilateral triangles in a square", "title": "Equilateral Triangles in a Square", "date": "2018-11-12", "statement": "Two equilateral triangles in a square. What's the missing area?", "categories": [ "Shapes" ], "techniques": [ "equilateral triangle" ], "drawing": "equilateral-triangles-in-a-square.lgf" }, { "slug": "three-aligned-triangles", "name": "three aligned triangles", "title": "Three Aligned Triangles", "date": "2018-11-11", "statement": "Given the areas of the three equilateral triangles, find the shaded area.", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-aligned-triangles.lgf" }, { "slug": "crossed-hexagon", "name": "crossed hexagon", "title": "Crossed Hexagon", "date": "2018-11-10", "statement": "What fraction of the regular hexagon is shaded?", "categories": [ "Shapes", "Transformations and Symmetry" ], "techniques": [ "trapezium" ], "drawing": "crossed-hexagon.lgf" }, { "slug": "square-in-a-semi-circle-in-a-square", "name": "square in a semi-circle in a square", "title": "Square in a Semi-Circle in a Square", "date": "2018-11-08", "statement": "What fraction of the larger square is covered by the one inside the semicircle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "square-in-a-semi-circle-in-a-square.lgf" }, { "slug": "two-equilateral-triangles-in-a-semi-circle", "name": "two equilateral triangles in a semi-circle", "title": "Two Equilateral Triangles in a Semi-Circle", "date": "2018-11-07", "statement": "There are two equilateral triangles inside this semicircle. What's the area of the larger one?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "two-equilateral-triangles-in-a-semi-circle.lgf" }, { "slug": "three-squares-in-a-circle", "name": "three squares in a circle", "title": "Three Squares in a Circle", "date": "2018-11-05", "statement": "Three squares in a circle ... If the blue triangle has area $5$, what's the area of the red triangle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "three-squares-in-a-circle.lgf", "live": true }, { "slug": "square-in-a-circle-in-a-quarter-circle-in-a-square", "name": "square in a circle in a quarter circle in a square", "title": "Square in a Circle in a Quarter Circle in a Square", "date": "2018-11-04", "statement": "There are three squares here. The smallest has area $4$. What's the missing area?", "categories": [ "Shapes" ], "techniques": [ "square" ], "drawing": "square-in-a-circle-in-a-quarter-circle-in-a-square.lgf" }, { "slug": "triangle-in-a-circle-in-a-quarter-circle-in-a-square", "name": "triangle in a circle in a quarter circle in a square", "title": "Triangle in a Circle in a Quarter Circle in a Square", "date": "2018-11-04", "statement": "The area of the small square is $4$. What’s the area of the triangle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "triangle-in-a-circle-in-a-quarter-circle-in-a-square.lgf" }, { "slug": "arcs-inside-a-triangle", "name": "arcs inside a triangle", "title": "Arcs Inside a Triangle", "date": "2018-11-02", "statement": "Two arcs are drawn from corners of the green equilateral triangle, which has area $3$. What's the area of the blue equilateral triangle?", "categories": [ "Measures" ], "techniques": [], "drawing": "arcs-inside-a-triangle.lgf" }, { "slug": "quadrilateral-from-two-squares-in-a-square", "name": "quadrilateral from two squares in a square", "title": "Quadrilateral from Two Squares in a Square", "date": "2018-10-30", "statement": "Join the four points where the inner squares touch the outer square to make a quadrilateral. What’s its area?", "categories": [ "Shapes" ], "techniques": [], "drawing": "quadrilateral-from-two-squares-in-a-square.lgf", "live": true }, { "slug": "triangle-centres-and-square-corners", "name": "triangle centres and square corners", "title": "Triangle Centres and Square Corners", "date": "2018-10-29", "statement": "The corners of the red square are at the centres of the equilateral triangles. What's the total shaded area?", "categories": [ "Shapes" ], "techniques": [], "drawing": "triangle-centres-and-square-corners.lgf" }, { "slug": "hexagon-and-concentric-circles", "name": "hexagon and concentric circles", "title": "Hexagon and Concentric Circles", "date": "2018-10-28", "statement": "The regular hexagon has a side length of $3$, and the rings are equally spaced. What's the total shaded area?", "categories": [ "Shapes" ], "techniques": [], "drawing": "hexagon-and-concentric-circles.lgf" }, { "slug": "chord-and-annulus", "name": "chord and annulus", "title": "Chord and Annulus", "date": "2018-10-27", "statement": "The four dots are equally spaced. What's the shaded area?", "categories": [ "Measures", "Circle Theorems" ], "techniques": [ "Pythagoras", "intersecting chords theorem" ], "drawing": "chord-and-annulus.lgf", "live": true }, { "slug": "dissected-hexagon", "name": "dissected hexagon", "title": "Dissected Hexagon", "date": "2018-10-26", "statement": "What fraction of this regular hexagon is not covered by the two isosceles triangles?", "categories": [ "Shapes" ], "techniques": [], "drawing": "dissected-hexagon.lgf" }, { "slug": "circles-in-rhombii-sequal", "name": "circles in rhombii sequal", "title": "Circles in Rhombii Sequel", "date": "2018-10-26", "statement": "A follow up question: hopefully by now you can convince yourself that the red circle covers a greater proportion of the rhombus than the two blue circles. So can you construct a different rhombus where these proportions would be equal?", "categories": [], "techniques": [], "drawing": "circles-in-rhombii-sequal.lgf", "live": true }, { "slug": "circles-in-triangle-and-rhombus", "name": "circles in triangle and rhombus", "title": "Circles in Triangle and Rhombus", "date": "2018-10-25", "statement": "The circle inside the equilateral triangle has area $16$. What's the area of the circle inside the rhombus?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "circles-in-triangle-and-rhombus.lgf" }, { "slug": "circles-resting-on-triangles", "name": "circles resting on triangles", "title": "Circles Resting on Triangles", "date": "2018-10-24", "statement": "Two semicircles are balanced on these three identical triangles. What's the missing area?", "categories": [ "Shapes" ], "techniques": [], "drawing": "circles-resting-on-triangles.lgf", "live": true }, { "slug": "arbelos", "name": "arbelos", "title": "Arbelos", "date": "2018-10-23", "statement": "The red line, of length $2$, is perpendicular to the bases of the three semicircles. What's the total shaded area?", "categories": [ "Circle Theorems" ], "techniques": [ "intersecting chords theorem" ], "drawing": "arbelos.lgf", "live": true }, { "slug": "four-circles-in-a-triangle-in-a-circle", "name": "four circles in a triangle in a circle", "title": "Four Circles in a Triangle in a Circle", "date": "2018-10-22", "statement": "Four identical circles are packed into an equilateral triangle. What fraction of the larger circle is shaded?", "categories": [ "Shapes" ], "techniques": [ "equilateral triangle" ], "drawing": "four-circles-in-a-triangle-in-a-circle.lgf" }, { "slug": "triangles-with-a-parallelogram", "name": "triangles with a parallelogram", "title": "Triangles with a Parallelogram", "date": "2018-10-21", "statement": "What's the area of the parallelogram?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "triangles-with-a-parallelogram.lgf", "live": true }, { "slug": "three-squares-in-a-square", "name": "three squares in a square", "title": "Three Squares in a Square", "date": "2018-10-18", "statement": "Three equal squares are packed into this bigger square. What's the shaded area?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "similarity" ], "drawing": "three-squares-in-a-square.lgf" }, { "slug": "two-circles-in-an-equilateral-triangle", "name": "two circles in an equilateral triangle", "title": "Two Circles in an Equilateral Triangle", "date": "2018-10-17", "statement": "What’s the side length of this equilateral triangle? Both circles have area $3$.", "categories": [ "Shapes" ], "techniques": [ "equilateral triangle" ], "drawing": "two-circles-in-an-equilateral-triangle.lgf" }, { "slug": "semi-circles-in-a-square", "name": "semi-circles in a square", "title": "Semi-Circles in a Square", "date": "2018-10-15", "statement": "If the radius of each semicircle is $5$, what's the total shaded area?", "categories": [ "Measures" ], "techniques": [ "dissection" ], "drawing": "semi-circles-in-a-square.lgf" }, { "slug": "five-rectangles-in-a-square", "name": "five rectangles in a square", "title": "Five Rectangles in a Square", "date": "2018-10-14", "statement": "What fraction of the square is covered by these $5$ identical rectangles?", "categories": [ "Shapes" ], "techniques": [ "square" ], "drawing": "five-rectangles-in-a-square.lgf" }, { "slug": "five-overlapping-circles", "name": "five overlapping circles", "title": "Five Overlapping Circles", "date": "2018-10-11", "statement": "What's the area of the smallest circle?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "five-overlapping-circles.lgf" }, { "slug": "four-regular-polygons", "name": "four regular polygons", "title": "Four Regular Polygons", "date": "2018-10-08", "statement": "The area of two of these regular polygons has been given. Can you find the area of the red triangle?", "categories": [ "Transformations and Symmetry" ], "techniques": [ "congruent", "transformation" ], "drawing": "four-regular-polygons.lgf", "live": true }, { "slug": "four-squares-around-a-quadrilateral", "name": "four squares around a quadrilateral", "title": "Four Squares Around a Quadrilateral", "date": "2018-10-07", "statement": "The four squares enclose a quadrilateral of area $10$. What's the total shaded area?", "categories": [ "Shapes", "Trigonometry" ], "techniques": [ "triangle", "sine rule" ], "drawing": "four-squares-around-a-quadrilateral.lgf", "live": true }, { "slug": "two-perpendicular-equilateral-triangles", "name": "two perpendicular equilateral triangles", "title": "Two Perpendicular Equilateral Triangles", "date": "2018-10-06", "statement": "The medians of these two equilateral triangles are perpendicular. What’s the area of the larger circle?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "two-perpendicular-equilateral-triangles.lgf" }, { "slug": "nested-circles-and-polygons-ii", "name": "nested circles and polygons ii", "title": "Nested Circles and Polygons II", "date": "2018-10-05", "statement": "Both polygons are regular. What fraction of the design is shaded?", "categories": [ "Shapes" ], "techniques": [], "drawing": "nested-circles-and-polygons-ii.lgf" }, { "slug": "spiralling-semi-circles", "name": "spiralling semi-circles", "title": "Spiralling Semi-Circles", "date": "2018-10-03", "statement": "$10$ equally spaced dots are joined by semicircles to make this spiral. Is more of it shaded red or orange? By how much?", "categories": [ "Measures" ], "techniques": [], "drawing": "spiralling-semi-circles.lgf" }, { "slug": "five-decreasing-squares", "name": "five decreasing squares", "title": "Five Decreasing Squares", "date": "2018-10-01", "statement": "What fraction of the largest square is shaded?", "categories": [ "Measures" ], "techniques": [ "Pythagoras", "dissection" ], "drawing": "five-decreasing-squares.lgf" }, { "slug": "triangle-and-semi-circle-in-a-circle", "name": "triangle and semi-circle in a circle", "title": "Triangle and Semi-Circle in a Circle", "date": "2018-09-29", "statement": "The semicircle and equilateral triangle have the same base. What fraction of the circle is shaded?", "categories": [ "Shapes" ], "techniques": [], "drawing": "triangle-and-semi-circle-in-a-circle.lgf" }, { "slug": "subdivided-parallelogram", "name": "subdivided parallelogram", "title": "Subdivided Parallelogram", "date": "2018-09-27", "statement": "Unshaded triangles are isosceles. What fraction of the parallelogram is shaded?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "subdivided-parallelogram.lgf" }, { "slug": "triangle-in-four-rectangles", "name": "triangle in four rectangles", "title": "Triangle in Four Rectangles", "date": "2018-09-26", "statement": "The four rectangles each have area $12$. What's the area of the triangle?", "categories": [ "Shapes" ], "techniques": [], "drawing": "triangle-in-four-rectangles.lgf", "live": true }, { "slug": "circle-in-a-trapezium", "name": "circle in a trapezium", "title": "Circle in a Trapezium", "date": "2018-09-24", "statement": "What fraction of the trapezium is shaded?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "circle-in-a-trapezium.lgf", "live": true }, { "slug": "subdivided-triangle", "name": "subdivided triangle", "title": "Subdivided Triangle", "date": "2018-09-19", "statement": "Red segments have length $5$, and yellow segments have length $3$. What's the shaded area?", "categories": [ "Measures" ], "techniques": [], "drawing": "subdivided-triangle.lgf" }, { "slug": "two-circles-inside-a-square", "name": "two circles inside a square", "title": "Two Circles Inside a Square", "date": "2018-09-17", "statement": "Given the areas of the two circles inside this square, can you find the area of the rectangle?", "categories": [ "Shapes" ], "techniques": [ "square" ], "drawing": "two-circles-inside-a-square.lgf" }, { "slug": "concentric-semi-circles", "name": "concentric semi-circles", "title": "Concentric Semi-Circles", "date": "2018-09-16", "statement": "The leftmost square has area $4$. What's the area of the square on the right?", "categories": [ "Shapes", "Transformations and Symmetry" ], "techniques": [ "square", "similarity" ], "drawing": "concentric-semi-circles.lgf" }, { "slug": "shaded-spikes-in-a-hexagon", "name": "shaded spikes in a hexagon", "title": "Shaded Spikes in a Hexagon", "date": "2018-09-14", "statement": "What fraction is shaded? The hexagon is regular, with equally spaced dots around its perimeter.", "categories": [ "Shapes", "Measures" ], "techniques": [], "drawing": "shaded-spikes-in-a-hexagon.lgf" }, { "slug": "squares-in-an-octagon", "name": "squares in an octagon", "title": "Squares in an Octagon", "date": "2018-09-11", "statement": "Pink lines have length $8$. What's the perimeter of the shaded octagon?", "categories": [ "Measures", "Transformations and Symmetry" ], "techniques": [ "Pythagoras", "symmetry" ], "drawing": "squares-in-an-octagon.lgf" }, { "slug": "four-squares-in-a-big-square", "name": "four squares in a big square", "title": "Four Squares in a Big Square", "date": "2018-09-09", "statement": "Squares of the same colour are the same size. What's the total shaded area?", "categories": [ "Shapes" ], "techniques": [ "square" ], "drawing": "four-squares-in-a-big-square.lgf" }, { "slug": "stacked-boxes-in-circles-in-squares", "name": "stacked boxes in circles in squares", "title": "Stacked Boxes in Circles in Squares", "date": "2018-09-08", "statement": "If the area of each pink square is $1$, what’s the area of the blue squares in each box as the sequence continues? Is the total area of the blue squares finite?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "stacked-boxes-in-circles-in-squares.lgf" }, { "slug": "four-stacked-squares-in-a-circle-in-a-square", "name": "four stacked squares in a circle in a square", "title": "Four Stacked Squares in a Circle in a Square", "date": "2018-09-08", "statement": "What fraction of the big square is shaded? Shaded squares are identical.", "categories": [ "Circle Theorems" ], "techniques": [ "intersecting chords theorem" ], "drawing": "four-stacked-squares-in-a-circle-in-a-square.lgf", "live": true }, { "slug": "overlapping-square-and-circle", "name": "overlapping square and circle", "title": "Overlapping Square and Circle", "date": "2018-09-06", "statement": "What's the area of the square?", "categories": [ "Circle Theorems" ], "techniques": [ "intersecting chords theorem" ], "drawing": "overlapping-square-and-circle.lgf" }, { "slug": "two-circles-inscribed-in-triangles-in-a-semi-circle", "name": "two circles inscribed in triangles in a semi-circle", "title": "Two Circles Inscribed in Triangles in a Semi-Circle", "date": "2018-09-03", "statement": "A circle of area $8$ is inscribed in an equilateral triangle. What's the area of the other circle?", "categories": [ "Shapes" ], "techniques": [ "equilateral triangle" ], "drawing": "two-circles-inscribed-in-triangles-in-a-semi-circle.lgf" }, { "slug": "arcs-in-a-circle", "name": "arcs in a circle", "title": "Arcs in a Circle", "date": "2018-09-01", "statement": "What fraction is shaded? Three coloured dots are equally spaced around the circle, with an arc (of the same colour) centred on each dot. The other arcs intersect at the centre of the circle.", "categories": [ "Shapes" ], "techniques": [], "drawing": "arcs-in-a-circle.lgf" }, { "slug": "six-squares-in-a-hexagon", "name": "six squares in a hexagon", "title": "Six Squares in a Hexagon", "date": "2018-08-31", "statement": "Six identical squares and a smaller rectangle are fitted into this regular hexagon. What fraction of the hexagon do they cover?", "categories": [ "Shapes" ], "techniques": [], "drawing": "six-squares-in-a-hexagon.lgf" }, { "slug": "four-equilateral-triangles-round-a-square", "name": "four equilateral triangles round a square", "title": "Four Equilateral Triangles Round a Square", "date": "2018-08-30", "statement": "Four equilateral triangles are arranged around a square which has area $12$. What's the total shaded area?", "categories": [ "Shapes" ], "techniques": [ "equilateral triangle" ], "drawing": "four-equilateral-triangles-round-a-square.lgf" }, { "slug": "two-triangles-in-a-rectangle", "name": "two triangles in a rectangle", "title": "Two Triangles in a Rectangle", "date": "2018-08-29", "statement": "Show that the two shaded areas cover the same proportion of the rectangle.", "categories": [ "Shapes", "Transformations and Symmetry" ], "techniques": [ "triangle" ], "drawing": "two-triangles-in-a-rectangle.lgf", "live": true }, { "slug": "two-overlapping-squares-iii", "name": "two overlapping squares iii", "title": "Two Overlapping Squares III", "date": "2018-08-28", "statement": "Is more of this design green or blue (and by how much)?", "categories": [ "Transformations and Symmetry", "Other Techniques" ], "techniques": [ "invariance principle" ], "drawing": "two-overlapping-squares-iii.lgf", "live": true }, { "slug": "two-isosceles-triangles", "name": "two isosceles triangles", "title": "Two Isosceles Triangles", "date": "2018-08-28", "statement": "These two isosceles triangles have the same area. What's the angle?", "categories": [ "Shapes" ], "techniques": [], "drawing": "two-isosceles-triangles.lgf" }, { "slug": "four-isosceles-triangles-in-a-circle", "name": "four isosceles triangles in a circle", "title": "Four Isosceles Triangles in a Circle", "date": "2018-08-26", "statement": "All four triangles are isosceles. What's the angle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "four-isosceles-triangles-in-a-circle.lgf" }, { "slug": "two-octagons-and-two-squares", "name": "two octagons and two squares", "title": "Two Octagons and Two Squares", "date": "2018-08-25", "statement": "The two regular octagons are concentric. Find [the] relationship between the two squares.", "categories": [ "Measures" ], "techniques": [], "drawing": "two-octagons-and-two-squares.lgf" }, { "slug": "hexagon-in-a-star-in-a-hexagon", "name": "hexagon in a star in a hexagon", "title": "Hexagon in a Star in a Hexagon", "date": "2018-08-24", "statement": "Corresponding sides of the two regular hexagons are parallel. If the small hexagon has an area of $18$, what's the shaded area?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "hexagon-in-a-star-in-a-hexagon.lgf" }, { "slug": "stacked-hexagons", "name": "stacked hexagons", "title": "Stacked Hexagons", "date": "2018-08-23", "statement": "Two of the regular hexagons are identical; the third has an area $10$. What's the area of the red triangle?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "stacked-hexagons.lgf" }, { "slug": "a-square-triangle-and-circle-in-a-square", "name": "a square, triangle, and circle in a square", "title": "A Square, Triangle, and Circle in a Square", "date": "2018-08-22", "statement": "The square, circle and triangle are stacked inside a larger square. What's the area of the circle?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "a-square-triangle-and-circle-in-a-square.lgf" }, { "slug": "region-of-an-octagon", "name": "region of an octagon", "title": "Region of an Octagon", "date": "2018-08-21", "statement": "The shaded area has the same value as the perimeter of the regular octagon. What is this value?", "categories": [ "Shapes" ], "techniques": [], "drawing": "region-of-an-octagon.lgf" }, { "slug": "semi-circle-in-a-square", "name": "semi-circle in a square", "title": "Semi-Circle in a Square", "date": "2018-08-20", "statement": "Is more of this square pink or blue? How would you prove it?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "semi-circle-in-a-square.lgf" }, { "slug": "polygons-with-equal-perimeter", "name": "polygons with equal perimeter", "title": "Polygons with Equal Perimeter", "date": "2018-08-19", "statement": "These regular polygons have the same perimeter. Find the ratio of the area of the circles.", "categories": [ "Shapes" ], "techniques": [], "drawing": "polygons-with-equal-perimeter.lgf" }, { "slug": "stacked-shapes", "name": "stacked shapes", "title": "Stacked Shapes", "date": "2018-08-19", "statement": "The triangles are equilateral, and the rectangles are twice as long as they are wide. If the area of the semicircle is $4$, what's the area of the pink circle?", "categories": [ "Shapes" ], "techniques": [ "equilateral triangle" ], "drawing": "stacked-shapes.lgf" }, { "slug": "four-squares-overlapping-a-circle", "name": "four squares overlapping a circle", "title": "Four Squares Overlapping a Circle", "date": "2018-08-17", "statement": "What's the area of the circle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "four-squares-overlapping-a-circle.lgf" }, { "slug": "triangle-in-circle-in-triangle-in-semi-circle", "name": "triangle in circle in triangle in semi-circle", "title": "Triangle in Circle in Triangle in Semi-Circle", "date": "2018-08-15", "statement": "A triangle in a circle in a triangle in a semicircle ... what's the angle?", "categories": [ "Circle Theorems" ], "techniques": [], "drawing": "triangle-in-circle-in-triangle-in-semi-circle.lgf", "live": true }, { "slug": "bell-ringing-braids", "name": "bell-ringing braids", "title": "Bell-Ringing Braids", "date": "2018-08-14", "statement": "From one row to the next, each point swaps with the neighbour it didn’t swap with last time. What percentage of the grid is enclosed by the red and orange lines? By red and yellow? By other pairs of colours?", "categories": [ "Shapes" ], "techniques": [ "trapezium" ], "drawing": "bell-ringing-braids.lgf" }, { "slug": "four-equilateral-triangles", "name": "four equilateral triangles", "title": "Four Equilateral Triangles", "date": "2018-08-13", "statement": "Here are $4$ equilateral triangles. Find the missing area.", "categories": [ "Shapes", "Transformations and Symmetry" ], "techniques": [ "equilateral triangle" ], "drawing": "four-equilateral-triangles.lgf" }, { "slug": "three-squares-and-two-equilateral-triangles", "name": "three squares and two equilateral triangles", "title": "Three Squares and Two Equilateral Triangles", "date": "2018-08-13", "statement": "$3$ squares, $2$ equilateral triangles. What's the pink area?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "three-squares-and-two-equilateral-triangles.lgf" }, { "slug": "zig-zag-triangles", "name": "zig-zag triangles", "title": "Zig-zag Triangles", "date": "2018-08-12", "statement": "The yellow triangles are all right-angled. What fraction is orange?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "zig-zag-triangles.lgf", "live": true }, { "slug": "squares-meeting-in-a-circle", "name": "squares meeting in a circle", "title": "Squares Meeting in a Circle", "date": "2018-08-12", "statement": "The two squares are identical, and the pink line is a diameter of the circle. What's the area of the pink triangle?", "categories": [ "Measures" ], "techniques": [], "drawing": "squares-meeting-in-a-circle.lgf", "live": true }, { "slug": "four-aligned-squares", "name": "four aligned squares", "title": "Four Aligned Squares", "date": "2018-08-10", "statement": "The area of the bottom left square is $5$. What's the area of the blue triangle?", "categories": [ "Shapes" ], "techniques": [ "triangle" ], "drawing": "four-aligned-squares.lgf", "live": true }, { "slug": "three-aligned-squares", "name": "three aligned squares", "title": "Three Aligned Squares", "date": "2018-08-09", "statement": "The sides lengths of the three squares are consecutive integers. What's the total area?", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "three-aligned-squares.lgf" }, { "slug": "lengths-in-a-crossed-trapezium", "name": "lengths in a crossed trapezium", "title": "Lengths in a Crossed Trapezium", "date": "2018-08-09", "statement": "In this right-angled trapezium, the green area is $6$ more than the yellow area. What's the length of the sloping side?", "categories": [ "Transformations and Symmetry" ], "techniques": [], "drawing": "lengths-in-a-crossed-trapezium.lgf", "live": true }, { "slug": "overlapping-squares", "name": "overlapping squares", "title": "Overlapping Squares", "date": "2018-08-08", "statement": "The numbers show the areas of the overlapping squares. What's the difference between the areas of the red and purple triangles?", "categories": [ "Measures" ], "techniques": [], "drawing": "overlapping-squares.lgf" }, { "slug": "toppled-square", "name": "toppled square", "title": "Toppled Square", "date": "2018-08-07", "statement": "What's the area of the toppled square?", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3lbmcqmy4nk22", "categories": [ "Measures" ], "techniques": [ "Pythagoras" ], "drawing": "toppled-square.lgf" }, { "slug": "two-rectangles-overlapping-a-circle", "name": "two rectangles overlapping a circle", "title": "Two Rectangles Overlapping a Circle", "date": "2018-08-02", "statement": "Which is the larger area: red or orange? The points around the circumference are evenly spaced.", "categories": [ "Shapes" ], "techniques": [], "drawing": "two-rectangles-overlapping-a-circle.lgf" }, { "slug": "subdivided-circles", "name": "subdivided circles", "title": "Subdivided Circles", "date": "2018-05-21", "statement": "What fraction of each circle is shaded? The $12$ dots are equally spaced, and the only point used inside the circle is the centre.", "thread": "https://bsky.app/profile/catrionaagg.bsky.social/post/3lb5tjlynec2u", "categories": [ "Measures" ], "techniques": [ "dissection" ], "drawing": "subdivided-circles.lgf" } ] }