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# A regular octagon with side lengths of 5.5 inches has an apothem length of 3 inches

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A regular octagon with side lengths of 5.5 inches has an apothem length of 3 inches

What is the area of this figure in square inches

May 4, 2020

#1
+769
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The area of a regular octagon is given by the formula $$A = 2s^2(1 + \sqrt{2})$$, where $$s$$ is the side length of the octagon.

We know that $$s = 5.5\text{ in}$$, so we just plug in that value into the equation to get:

$$A = 2(5.5^2)(1 + \sqrt{2})$$

$$A = 60.5(1 + \sqrt{2})$$

$$A = 60.5 + 60.5(1.414)$$

$$A = 60.5 + 85.547 = \fbox{146.047 \text{ in}^2}$$ :D

May 4, 2020
#2
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I thought it was just 60 inches^2

May 4, 2020