# The area of a regular hexagon is 1500 square centimeters. What is its perimeter? Please show working.

##### 2 Answers

The perimeter is approximately

#### Explanation:

A regular hexagon consists of 6 congruent equilateral triangles, so its area can be calculated as:

The area is given, so we can solve an equation:

to find the length of the hexagon's side

Multiplying by

Dividing by

For further calculations I take approximate value of

So the equality becomes:

Now we can calculate the perimeter:

#### Explanation:

The hexagon can be split into 6 equilateral triangle.

Each triangle has area of

If the length of each triangle is

Looking at 1 triangle, the area is given by half x base x height.

The base is