A regular hexagon containing an orange quadrilateral. What fraction of the total area is blue?
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The Sikh turban
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The honeycomb
Two regular hexagons inscribed in a square. If the hexagons have side length a and b, what is the square’s side length?
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The folded napkin
A square sheet of paper is folded symmetrically from a corner. If the fold length is 4, what is the area of the triangle formed by the other three corners?
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Together we stand
Two squares sharing a vertex. What’s the angle α?
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The pleasure dome
A semicircle with three squares. The areas of the smaller squares are given. What is the area of the biggest one?
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Twin peaks
A rectangle with three line segments. What is the proportion yellow : red?
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Pyramidion
A triangle containing a semicircle and an equilateral triangle. What fraction is golden?
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The ocean sunset
A semicircle is inscribed in a rectangle. What is the minimal covered fraction?
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Triple dice
An equilateral triangle with three congruent squares. What’s the angle α?
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Paper hat II
Two overlapping congruent right triangles. If |AB|=15 and |BC|=7, what is the total area?