Categories
Beginner

The Sikh turban

A regular hexagon containing an orange quadrilateral. What fraction of the total area is blue?

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Intermediate

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?

Categories
Intermediate

The pleasure dome

A semicircle with three squares. The areas of the smaller squares are given. What is the area of the biggest one?

Categories
Beginner

Twin peaks

A rectangle with three line segments. What is the proportion yellow : red?

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Intermediate

Pyramidion

A triangle containing a semicircle and an equilateral triangle. What fraction is golden?

Categories
Advanced

The ocean sunset

A semicircle is inscribed in a rectangle. What is the minimal covered fraction?

Categories
Intermediate

Paper hat II

Two overlapping congruent right triangles. If |AB|=15 and |BC|=7, what is the total area?

Categories
Intermediate

En garde

An isosceles triangle with two altitudes dividing each other in segments of length 4 and 5. What is the total triangle area?

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Advanced

The satellite

A circle containing three squares. What fraction is coloured?

Categories
Intermediate

Distant peaks

Two isosceles triangles and a right angle. What is the proportion green : gold?