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
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

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?

Categories
Advanced

The bigger picture

In a small square two perpendicular lines are drawn. A larger parallel square is constructed as shown. Prove it is a scaled copy of the smaller square but rotated 90° anticlockwise.

Categories
Intermediate

La Flèche Wallonne

A triangle is divided in four. What is the black area?

Categories
Intermediate

The attic room

A blue square is topped with a right triangle. Using line segments to the top, a green quadrilateral is constructed with at least two right angles. What is the area proportion green : blue?

Categories
Advanced

The flying banner

A triangle with a quadrilateral that covers half its area. What is the angle?

Categories
Intermediate

The paper hat

A rectangle and several triangles. The orange triangle has the same area as the green trapezium. What’s the total coloured fraction?

Categories
Beginner

The parquet floor

A unit rhombus is surrounded by four congruent parallelograms. All five quadrilaterals have equal area. What are the parallelogram sides x and y?