Two regular hexagons inscribed in a square. If the hexagons have side length a and b, what is the square’s side length?

# Tag: square

## 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?

## Together we stand

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

## The pleasure dome

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

## Triple dice

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

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

## The satellite

A circle containing three squares. What fraction is coloured?

## The Lion King II

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

## The dangling square

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

## The yellow sailboat

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