Question

a regular hexagon with center e is shown below. what is the area of the hexagon? round your answer to the nearest tenth. square centimeters

Explanation:

Step1: Find the area of one equilateral triangle

A regular hexagon can be divided into 6 equilateral triangles with side - length equal to the radius of the circum - circle. Here, the radius \(r = 8\) cm.
The area formula for an equilateral triangle is \(A_{\triangle}=\frac{\sqrt{3}}{4}a^{2}\), where \(a = 8\) cm.

$$A_{\triangle}=\frac{\sqrt{3}}{4}\times8^{2}=\frac{\sqrt{3}}{4}\times64 = 16\sqrt{3}\text{ cm}^2$$

Step2: Calculate the area of the hexagon

Since the area of the hexagon \(A = 6\times A_{\triangle}\)

$$A=6\times16\sqrt{3}=96\sqrt{3}$$

$$A\approx96\times1.732 = 166.3\text{ cm}^2$$

Answer:

\(166.3\)