Question

O is the center of the regular octagon below. Find its area. Round to the nearest tenth if necessary. O 6​

Answer 1

`\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=\cfrac{1}{2}nR^2\sin\left( (360)/(n) \right) ~~ \begin{cases} R=\stackrel{\textit{radius of}}{circumcircle}\\ n=\stackrel{\textit{number of}}{sides}\\[-0.5em] \hrulefill\\ n=8\\ R=6 \end{cases}\implies A=\cfrac{1}{2}(8)(6)^2\sin\left( (360)/(8) \right) \\\\\\ A=144\sin(45^o)\implies A=144\cdot \cfrac{√(2)}{2}\implies A=72√(2)\implies A\approx 101.8`