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

1 Answer

#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.