Question

A regular hexagon has side 2 meters. What is its area?

Answer 1

`6sqrt(3)"m"^2`

Explanation:

The hexagon can be divided into `6` equilateral triangles with base `2"m"` and height `sqrt(3)"m"`. Why `sqrt(3)"m"`? Each equilateral triangle can be split into two right angled triangles with hypotenuse `2"m"`, one leg `1"m"` and the other `sqrt(2^2-1^2)"m" = sqrt(3)"m"`.

The area of each of the equilateral triangles is:

`1/2 xx "base" xx "height" = 1/2 xx 2"m" xx sqrt(3)"m" = sqrt(3)"m"^2`

So the area of the hexagon is `6sqrt(3)"m"^2`