Question

How do you find the area of a regular octagon inscribed in a circle whose equation is given by (x-2)² + (y+3)² = 25?

Answer 1

`50sqrt(2)`

Explanation:

The radius of the circle is `5`. Each side of the regular octagon subtends `45^@` at the center.

The lines joining opposite vertices are diameters. These diameters divide the octagon into eight isosceles triangles. The equal sides of every triangle include `angle 45^@`. Their lengths are the radius of the circle `= 5`.

So, the area of each of these eight triangles is

`A_l = 1/2 * 5.5 * sin 45^@=25/(2sqrt(2))`

The area of the octagon is

`A_o = 8 * A_l`

`A_o = 8 * 25/(2sqrt(2))=50sqrt(2)`