Categories
Intermediate

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?

Categories
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

Together we stand

Two squares sharing a vertex. What’s the angle α?

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
Intermediate

Triple dice

An equilateral triangle with three congruent squares. What’s the angle α?

Categories
Beginner

The wall

Two congruent rectangles and squares. Proof that the four points are on one circle.

Categories
Advanced

The satellite

A circle containing three squares. What fraction is coloured?

Categories
Intermediate

The Lion King II

A regular hexagon and three squares. What is the proportion yellow : brown?

Categories
Beginner

The dangling square

Four squares and five shared vertices. If the orange area is 4, what is the green area?

Categories
Beginner

The yellow sailboat

A square, two equilateral triangles and an extended side. What is the proportion yellow : blue?