Categories
Advanced

The ocean sunset

A semicircle is inscribed in a rectangle. What is the minimal covered fraction?

Categories
Intermediate

Paper hat II

Two overlapping congruent right triangles. If |AB|=15 and |BC|=7, what is the total area?

Categories
Intermediate

En garde

An isosceles triangle with two altitudes dividing each other in segments of length 4 and 5. What is the total triangle area?

Categories
Advanced

The satellite

A circle containing three squares. What fraction is coloured?

Categories
Intermediate

Distant peaks

Two isosceles triangles and a right angle. What is the proportion green : gold?

Categories
Beginner

The blue pill

A regular octagon containing a blue hexagon. All line segments have equal length. What fraction is blue?

Categories
Intermediate

The Lion King II

A regular hexagon and three squares. What is the proportion yellow : brown?

Categories
Advanced

The eye mask

A right triangle with its inscribed circle. Two cevians are drawn through the circle centre. What is the circle area in terms of triangle areas A and B?

Categories
Intermediate

The red balloon

An equilateral triangle with an altitude. Two of its sides form the radii of the circular sector. What fraction of the area is covered by the red circle?

Categories
Beginner

The dangling square

Four squares and five shared vertices. If the orange area is 4, what is the green area?