Two squares and two given areas. What’s the total area?
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Out of the box
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The spotlight
A right triangle with two cevians. What’s the angle α?
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The lemon slice
A semicircle is inscribed in a quarter circle. What is the minimal yellow fraction?
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Connecting the dots
Three squares share three vertices which form a right triangle. Their centres are connected to form another triangle of which one side is given. What’s the blue area?
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Between the bars
Two parallel lines support two rectangles. Prove they have equal area.
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Mount Fuji
An equilateral triangle inscribed in a circle is divided by a diameter parallel to one of its sides. What is the proportion light : dark blue?
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The Magdeburg hemispheres
A square containing a circle and two semicircles, all three having the same radius. What fraction is purple?
Five unit squares inside a larger square. What is the total area?
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The axe head
A tetrahedron with given vertex coordinates. What is its volume?
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The sleeping bag
A semicircle containing a circle. One line segment is tangent to the circle and connects to the semicircle centre. The chord connects two tangency points. What fraction is blue?