Question

What is the area of a regular hexagon with a 48-inch perimeter?

Answer 1

`16 sqrt(3) approx 27.71` square inches.

Explanation:

First of all, if the perimeter of a regular hexagon measures `48` inches, then each of the `6` sides has to be `48/6=8` inches long.

To compute the area, you can divide the figure in equilateral triangles as follows.

Given the side `s`, the area of an equilateral triangle is given by `A=sqrt(3)/4 s^2` (you can prove this using the Pythagorean Theorem or trigonometry).

In our case `s=8` inches, so the area is `A=sqrt(3)/4 8^2=16 sqrt(3) approx 27.71` square inches.