Categories
Intermediate

The folded napkin

A square sheet of paper is folded symmetrically from a corner. If the fold length is 4, what is the area of the triangle formed by the other three corners?

Categories
Beginner

Twin peaks

A rectangle with three line segments. What is the proportion yellow : red?

Categories
Intermediate

Pyramidion

A triangle containing a semicircle and an equilateral triangle. What fraction is golden?

Categories
Intermediate

Triple dice

An equilateral triangle with three congruent squares. What’s the angle α?

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
Intermediate

Distant peaks

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

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?