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

# Category: 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?

## 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?

## Pyramidion

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

## Triple dice

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

## Paper hat II

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

## En garde

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

## Distant peaks

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

## The Lion King II

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