Question

each side of the regular hexagon measures 8 cm. what is the area of the hexagon? 96√3 square centimeters 384√3 square centimeters 192√3 square centimeters 768√3 square centimeters

Explanation:

Step1: Divide hexagon into triangles

A regular hexagon can be divided into 6 equilateral triangles. Each side of the hexagon is the side - length of the equilateral triangle, so the side - length of each equilateral triangle $a = 8$ cm.

Step2: Find area of one equilateral triangle

The area formula of an equilateral triangle is $A_{\triangle}=\frac{\sqrt{3}}{4}a^{2}$. Substitute $a = 8$ cm into the formula: $A_{\triangle}=\frac{\sqrt{3}}{4}\times8^{2}=\frac{\sqrt{3}}{4}\times64 = 16\sqrt{3}$ square cm.

Step3: Find area of hexagon

Since the hexagon is composed of 6 such equilateral triangles, the area of the hexagon $A = 6\times A_{\triangle}=6\times16\sqrt{3}=96\sqrt{3}$ square cm.

Answer:

$96\sqrt{3}$ square centimeters