Categories
Beginner

The pine forest

A square containing a quarter circle. What’s the proportion blue : brown : green?

Categories
Intermediate

The red sash

Two squares and a rectangle. What is area of the rectangle in terms of square sides a and b?

Categories
Beginner

The star gazer

A square divided by a diagonal and another line segment. What fraction of its area is purple?

Categories
Advanced

The Eightfold Path

A semicircle, a square and an isosceles triangle. What’s the angle α?

Categories
Beginner

The iglo

A semicircle, a square and a chord. If the square has area 32, what is the semicircle area?

Categories
Beginner

The chess board

A square is divided by six line segments. What fraction is brown?

Categories
Beginner

Free four

A unit circle with an inscribed square and four semicircles. What’s the sum of the semicircle areas?

Categories
Advanced

As above, so below

A semicircle, a square, a triangle and two circles. A centre and a tangency point are highlighted. Prove that the circles are congruent.

Categories
Beginner

The sand heap

Two squares share a vertex. Three other vertices form a triangle, of which one side length is given. What is its area?

Categories
Beginner

The full circle

Two squares of area D and J share a vertex while the circle passes through four other vertices. What is the area of the latter in terms of D and J?