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A regular octagon (8-sided polygon) has an area of 690 sq. ft. and a side length of 20feet. Find the length of the apothem to the nearest foot.

A regular octagon (8-sided polygon) has an area of 690 sq. ft. and a side length of-example-1

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Given:


\begin{gathered} s=\text{side length} \\ s=20\text{ fe}et \\ a=\text{ apothem length} \\ n=\text{ number of sides of a polygon} \\ n=8 \end{gathered}

Apothem length.


a=(s)/(2\tan ((180)/(n)))
\begin{gathered} a=(20)/(2\tan ((180)/(8))) \\ a=(20)/(2\tan (22.5)) \\ a=(20)/(2*0.4142) \\ a=(20)/(0.828) \\ a=24.142 \end{gathered}

Length of the apothem is 24.142

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