Question

question
find the area of the regular polygon. round to the nearest hundredths.
image of a regular octagon with an apothem of 10 yd and a side length of 8.28 yd

Explanation:

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

The formula for the area of a regular polygon is \(A=\frac{1}{2}aP\), where \(a\) is the apothem and \(P\) is the perimeter.

Step2: Determine the number of sides and find the perimeter

The given polygon is an octagon (\(n = 8\)). The length of one side \(s=8.28\) yd. The perimeter \(P=ns\), so \(P = 8\times8.28=66.24\) yd.

Step3: Identify the apothem

The apothem \(a = 10\) yd.

Step4: Calculate the area

Substitute \(a = 10\) and \(P=66.24\) into the formula \(A=\frac{1}{2}aP\).

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Answer:

\(331.20\) yd²