Question

each side of the regular hexagon below measures 8 cm. what is the area of the hexagon? 96\sqrt{3} square centimeters 192\sqrt{3} square centimeters 384\sqrt{3} square centimeters 768\sqrt{3} square centimeters

Explanation:

Step1: Analyze the regular hexagon

A regular hexagon can be divided into 6 equilateral triangles. Each side of the hexagon is \(a = 8\) cm.

Step2: Calculate the area of one equilateral triangle

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

Step3: Calculate the area of the hexagon

Since the hexagon is composed of 6 such equilateral triangles, \(A = 6\times A_{\triangle}\)
\(A=6\times16\sqrt{3}=96\sqrt{3}\) \(cm^{2}\)

Answer:

\(96\sqrt{3}\) square centimeters