On his blog MathWithBadDrawings, Ben Orlin reposted a couple of geometrical sangaku-like puzzles by math teacher Catriona Shearer. These are eleven of her personal favorites. If you dare, definitely give them a try!
Transit Across a Purple Sun. What’s the total shaded area?
Shearer’s Emerald. Four squares. What’s the shaded area?
The Pyramid with Two Tombs. Two squares inside an equilateral triangle. What’s the angle?
Setting Sun, Rising Moon. What fraction of the rectangle is shaded?
Hex Hex Six. Both hexagons are regular. How long is the pink line?
Four, Three, Two. What’s the area of this triangle?
The Trinity Quartet. All four triangles are equilateral. What fraction of the rectangle do they cover?
The Falling Domino. This design is made of three 2×1 rectangles. What fraction of it is shaded?
Slices in a Sector. The three colored sections here have the same area. What’s the total area of the square?
Disorientation. The right-angled triangle covers ¼ of the square. What fraction does the isosceles triangle cover?
Sunny Smile Up. What fraction of the circle is shaded?
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