Categories
Intermediate

The honeycomb

Two regular hexagons inscribed in a square. If the hexagons have side length a and b, what is the square’s side length?

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
Beginner

Darth Vader

A regular hexagon containing three diagonals and three congruent circular arcs. What fraction is black?

Categories
Intermediate

The swinging pyramid

A regular hexagon and two equilateral triangles share a vertex. What is the area proportion blue : yellow?

Categories
Intermediate

Boxcars

Two regular hexagons share two vertices. What fraction of the area is purple?

Categories
Intermediate

The egg basket

A regular hexagon with a diagonal and a line segment connecting a vertex to a point on the other side. The two triangle areas are given. What is the hexagon’s area?

Categories
Intermediate

The chef’s hat

Two regular hexagons connected by a rectangle. Prove that the five vertices lie on a circle.

Categories
Intermediate

The Lion King

Three unit squares form the skeleton of a hexagon. What’s the area of the yellow rectangle?

Categories
Beginner

The bobline

A regular hexagon is folded back and forth along the dotted line. What fraction of the area is yellow?