Categories
Beginner

The triangular tiling

A rectangle is divided into four similar triangles. What fraction is blue?

Categories
Intermediate

The righteous four

Four rectangles. The green and red rectangle are similar. What’s the area proportion of the orange and the blue rectangle?

Categories
Intermediate

The misfit

A rectangle is inscribed in a regular hexagon, covering 14/27 of its area. What is red : yellow : green?

Categories
Intermediate

Five to twelve

A square and a rectangle share two vertices. If the square has twice the area of the rectangle, what’s the angle α?

Categories
Advanced

The maxbox

A square containing a red square of variable size sharing a vertex with a blue rectangle. What is the maximal blue fraction?

Categories
Intermediate

Lopsided

The apex of a parabola is the shared vertex of two rectangles. Proof that the rectangles are similar.

Categories
Advanced

The bell tolls

An equilateral triangle inscribed in a rectangle. What is its area X in terms of triangle areas A and B?

Categories
Beginner

The high seas

A rectangle containing four triangles. What is the total area?

Categories
Beginner

Overhanging rock

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

Categories
Intermediate

The secret document

One corner of a rectangular piece of paper is folded back and forth to the opposite side. What is the proportion red : blue?