Categories
Intermediate

The seventh bell

A regular hexagon shares a vertex with an equilateral triangle of area 7. What is the area of the hexagon?

Categories
Intermediate

Rising bread

A regular hexagon with a diagonal and a circular arc centred in a side midpoint. What fraction is yellow?

Categories
Beginner

The double bottom

A regular hexagon and a square share a vertex. What is the area proportion square : hexagon?

Categories
Beginner

Going halfway

A regular hexagon contains a diagonal, a green equilateral triangle and a red triangle. Prove that the latter is isosceles.

Categories
Intermediate

The seesaw

A regular hexagon with three diagonals and two line segments at right angles. What is the proportion green : yellow : blue : orange?

Categories
Intermediate

The Zamani suggestion

Two regular hexagons share a vertex. What’s the area proportion red : yellow hexagon?

Categories
Beginner

Squaring a rectangle

A regular hexagon, a square and a rectangle. What is the area proportion rectangle : square?

Categories
Intermediate

The misfit

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

Categories
Beginner

The pit

A regular hexagon, a square with its diagonals, an equilateral triangle and a circle. Prove that the hexagon and the circle are concentric.

Categories
Intermediate

The dance

A regular hexagon, two squares and a semicircle connecting two vertices. Is the red vertex located on the semicircle?