Question

A regular octagon is inscribed in a circle of radius r. Show that the area of the octagon is 2 root 2r^2

Answer 1

Use the law of sines to find the area of each of the 8 triangles that form the octagon. Multiply by 8 and you are done.

Answer 2

\[
\frac{8}{2} r^2 \sin \left(\frac{2 \pi }{8}\right)=4 r^2 \sin
\left(\frac{\pi }{4}\right)=\frac{4 \sqrt{2} r^2}{2}=2 \sqrt{2}
r^2

\]