Question

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what is the exact area of a regular hexagon with side length of 16 inches?
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in²
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Explanation:

Step1: Divide the regular hexagon into six equilateral triangles

A regular hexagon can be divided into six congruent equilateral triangles. The side length of each equilateral triangle is \(a = 16\) inches.

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 \(a = 16\) into the formula: \(A_{\triangle}=\frac{\sqrt{3}}{4}\times16^{2}=\frac{\sqrt{3}}{4}\times256 = 64\sqrt{3}\) square inches.

Step3: Calculate the area of the regular hexagon

Since the area of the regular hexagon \(A = 6\times A_{\triangle}\), substitute \(A_{\triangle}=64\sqrt{3}\) into the formula. Then \(A=6\times64\sqrt{3}=384\sqrt{3}\) square inches.

Answer:

\(384\sqrt{3}\)