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New Year 2021

Three squares are placed as shown. Given that the green areas are equal, what is the side length of the orange square?

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An Italian hill

Two semicircles inside a rectangle. What is the proportion of the red to the green area?

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The radio telescope

A square contains two triangles. What fraction of the square do they cover?

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The warning triangle

An equilateral triangle contains three congruent rectangles. Two distances on its base are given. What fraction is white?

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The tumbler doll

A circle within an equilateral triangle within a circle. What fraction is shaded?

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The green kimono

An equilateral triangle and three squares. What’s the angle?

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The circus tent

A regular octagon is coloured as shown. What fraction of its area is red?

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The windshield wipers

A square and two rectangles, connected by two circular arcs, form a square. What is the proportion of the orange to the green area?

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The square peg

A square is fitted into an equilateral triangle as shown. What fraction is shaded?

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Beginner

The velocipede

Two circles are embedded in a frame of size 9 x 8. What is their total area?