Question

a regular pentagon is shown below.
5 ft.
what is the area of the pentagon?
round your answer to the nearest tenth.
square feet

Explanation:

Step1: Recall the formula for the area of a regular pentagon

The formula for the area \(A\) of a regular pentagon with side length \(s\) is \(A=\frac{1}{4}\sqrt{5(5 + 2\sqrt{5})}s^{2}\).

Step2: Substitute \(s = 5\) into the formula

First, calculate the value of \(\frac{1}{4}\sqrt{5(5 + 2\sqrt{5})}\).

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Then, since \(s = 5\), use \(A=\frac{1}{4}\sqrt{5(5 + 2\sqrt{5})}s^{2}\), so \(A=1.7205\times5^{2}\).

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$$

Answer:

\(43.0\) square feet