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A unit square, a semicircle, a right triangle and an isosceles triangle. What is the total purple area?

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## En bloc

Two similar rectangles. If the small one has area 4 what is the area of the large rectangle?

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## The tympanum

A regular pentagon with a diagonal and an extended side. What is the top angle of the isosceles triangle?

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## Giro d’Italia

A square with the origin halfway one of its sides. The coordinates of two vertices are given. What is the square’s area?

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## The Eye of Horus

A semicircle containing two equilateral triangles containing a circle. What fraction is blue?

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## The winged messenger

A semicircle and two quarter circles pass through the same point. What’s the angle α?

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## Hard on portside

Two squares and two diagonals. Two areas are given. What is the total area?

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## Points of authority

Three squares and three shared vertices. Prove the three red vertices are collinear.

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## The swinging pyramid

A regular hexagon and two equilateral triangles share a vertex. What is the area proportion blue : yellow?

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## The doors of perception

Two line segments and three rectangles, two of which have a given area. What is the yellow area?