Question

What is the area of a regular hexagon with a perimeter of 24?

Answer 1

Area is `24sqrt(3)`

Explanation:

First we have to calculate the side. Knowing the perimeter `P` we can write, that:

`a=P/6=24/6=4`

A regular hexagon can be divided to `6` identical equilateral triangles whose side's length is equal to the side of hexagon, so to calculate the area you can use the formula:

`A_h=6*A_t=6*((a^2sqrt(3))/4)=6*((16sqrt(3))/4)=24sqrt(3)`