Question

O is the center of the regular octagon below. Find its area. Round to the nearest tenth if necessary.

Answer 1

`\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=na^2\cdot \tan\left( (180)/(n) \right) ~~ \begin{cases} n=sides\\ a=apothem\\[-0.5em] \hrulefill\\ n=8\\ a=15 \end{cases}\implies A=(8)(15)^2\tan\left( (180)/(8) \right) \\\\\\ A=1800\tan(22.5^o)\implies A\approx 745.6`

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