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=\cfrac{nR^2}{2}\cdot \sin\left( (360)/(n) \right) ~~ \begin{cases} n=sides\\ R=\stackrel{\textit{radius of}}{circumcircle}\\[-0.5em] \hrulefill\\ n=8\\ a=17 \end{cases}\implies A=\cfrac{(8)(6)^2}{2}\cdot \sin\left( (360)/(8) \right) \\\\\\ A=144\sin(45^o)\implies A\approx 101.8`

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