## Shaded Hexagon

#### Problem

Two congruent equilateral triangles, each with an area equal to 36 cm^{2}, are placed on top of each other so that they form a regular hexagonal overlap.

Find the area of the hexagon.

#### Solution

The triangles can be split up as follows:

It can be seen that the shaded area is ^{6}/_{9} of one triangle, that is ^{2}/_{3} of 36 = 24 cm^{2}.

Must the triangles be equilateral?

What will the area of the overlap be if two squares, each with an area of 36 cm^{2}, are overlapped in the same way to form an octagon?

Is the octagon regular?

Problem ID: 149 (Feb 2004) Difficulty: 1 Star