# What is the area of this hexagon?

##### 1 Answer

Most likely, this question is about a *regular* hexagon with a given size

The answer is:

#### Explanation:

If we connect a center of a regular hexagon with all

The proof is trivial. Since this hexagon is regular, the distances from its center to all vertices are equal to each other. Hence, all these triangles are isosceles with a top being in the center of a hexagon.

In addition, an angle at the top of each triangle is

Two other angles of each triangle, therefore, are also equal to

That makes each isosceles triangle an equilateral one.

An equilateral triangle with a side

Therefore, its area is

The area of a hexagon in