A square and a rectangle share a vertex. Two triangle areas are given. What is the total area?

# Category: Beginner

## The pentagon attack

Two regular pentagons and two diagonals. What’s the angle α?

## Confined enclosure

A square containing four smaller squares. What fraction of its area is orange?

## Lean on me

Two squares and two diagonals. Prove that the angles α and β are equal.

## The dolphin

Two semicircles, a tangent and an altitude to the tangency point. Prove that the red triangle is isosceles.

## Parallelism

A trapezium with its diagonals and a parallel line segment. What’s the proportion blue : red?

## The Common Brimstone

A square divided by three line segments. What’s the proportion green : yellow?

## Tension control

Three squares and a line segment of which a vertex is the midpoint. What is the proportion purple : green?

## The pyramid scheme

Two congruent circles and a triangle. Prove that the triangle is isosceles.

## The French kiss

Two tangent circles and two red tangent line segments. The three tangency points are shown. What is the angle β in terms of the angle α?