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?

Categories
Intermediate

Giro d’Italia

A square with the origin halfway one of its sides. The coordinates of two vertices are given. What is the square’s area?

Categories
Intermediate

Hard on portside

Two squares and two diagonals. Two areas are given. What is the total area?

Categories
Advanced

Points of authority

Three squares and three shared vertices. Prove the three red vertices are collinear.

Categories
Intermediate

The crane

A triangle with an inscribed square. What fraction is yellow?

Categories
Advanced

The balancing block

A rectangle inside a square. One of its sides is tangent to the quarter circle. What fraction is green as x approaches 0?