A rectangle and a square. What is the proportion purple : blue?

# Author: Rik

## The hourglass

A rectangle with two crossing line segments. What’s the minimal shaded fraction?

Four quarter circles of radius 1, each containing a square. What is the blue area?

## Below the tree line

A triangle is split in two. What is the area of the green quadrilateral in terms of lengths a and b?

## Tympanum II

A regular pentagon with a diagonal. What is the top angle of the isosceles triangle?

## The pillbox

Three touching circles in a rectangle and a common tangent. What’s the angle?

## The ramp

A right triangle is split in two. What is the maximum yellow fraction?

## The headphones

A unit square, a semicircle, a right triangle and an isosceles triangle. What is the total purple area?

Two similar rectangles. If the small one has area 4 what is the area of the large rectangle?

## The tympanum

A regular pentagon with a diagonal and an extended side. What is the top angle of the isosceles triangle?