Categories
Beginner

The hammock

A square inscribed in a triangle. Two areas are given. What is the square’s area?

Categories
Intermediate

Lazy Friday

Four congruent squares plus another one. What is the angle α?

Categories
Intermediate

The fez

A circle and a semicircle inside a square. What’s the length proportion of the two chords?

Categories
Advanced

The orange belt

Three squares and three shared vertices. Prove that the orange quadrilateral is in fact a parallelogram.

Categories
Intermediate

The cleaver

Four squares, a rectangle and a circle. What is the proportion brown : grey?

Categories
Beginner

The green field

A square is divided in two quadrilaterals of given area. What fraction of the square’s perimeter is red?

Categories
Intermediate

The twin triangles

Two squares share a vertex. Prove that the red triangle is congruent to the blue one.

Categories
Intermediate

Ice cube

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

Categories
Beginner

Papillon

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

Categories
Beginner

The headphones

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