Chapter 14, Problem 8MCE

To determine

Tofind: the area of the regular hexagon.

Answer to Problem 8MCE

The area of the regular hexagon is $24\sqrt{3}$ .

Explanation of Solution

Given information:

The perimeter of the regular hexagon is $24$ .

Calculation: to find area of the hexagon, first find the side of the hexagon,

Let $x$ is the side of the hexagon,

Since, perimeter is $24$ ,

$\begin{array}{l}6x=24\\ x=4\text{ [divide]}\end{array}$

To find the area of hexagon, substitute in the formula and then simplify,

$\begin{array}{l}A=\frac{3\sqrt{3}}{2}{x}^2\\ A=\frac{3\sqrt{3}}{2}{\left(4\right)}^2\text{ [substitute]}\\ A=24\sqrt{3}\text{ [simplify]}\end{array}$

Thus, the area of hexagon is $24\sqrt{3}$ .