Question

a regular hexagon has a radius of 20 in. what is the approximate area of the hexagon?
600 in²
1,038 in²
1,200 in²
2,076 in²

Explanation:

Step1: Divide the hexagon into equilateral triangles

A regular hexagon can be divided into 6 equilateral triangles. The radius of the hexagon is equal to the side length of each equilateral triangle. So, the side length \(a = 20\) in.

Step2: Calculate the area of one equilateral triangle

The area formula for an equilateral triangle is \(A_{\triangle}=\frac{\sqrt{3}}{4}a^{2}\). Substitute \(a = 20\) into the formula:

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Step3: Calculate the area of the hexagon

Since the hexagon is composed of 6 equilateral triangles, the area of the hexagon \(A = 6A_{\triangle}\).

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Answer:

\(1,038\space in^{2}\) (the closest value to the calculated \(1039.2\) among the given options)