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?

Categories
Beginner

The England win

A unit square containing two red overlapping congruent rectangles. If they cover exactly half the square’s area, what is their width x?

Categories
Intermediate

A nice percentage

An orange square and a blue rectangle with two congruent inscribed circles. What is the angle α?

Categories
Advanced

The sneak peek

A rectangle with given side lengths is folded back and forth such that the corner touches the opposite side as shown. What is the minimal shaded fraction?

Categories
Intermediate

House of Orange

A right triangle with a red and yellow square attached. Two circular arcs centered in the triangle vertices. What is the area of the orange rectangle in terms of red and yellow?

Categories
Intermediate

Take five origami

Divide a rectangular piece of paper in five pieces of equal area. You only have a pair of scissors at your disposal, but you are allowed to make straight folds to guide you.

Categories
Beginner

The voting pencil

A square and a rectangle share a vertex. Two triangle areas are given. What is the total area?

Categories
Intermediate

The yardstick

A rectangle containing a circle and a line segment connecting the top side to the bottom tangency point. What is its area in terms of lengths a and b?

Categories
Intermediate

The Suresh similarity

Two squares and a rectangle. Prove that the red triangles are similar.