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?

##25sqrt2##

The radius of the circle is 5. Each side of the regular octagon subtends ##45^o## 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^o##. Their lengths are radius of the circle = 5.

So, the area of each of these eight triangles is ##(1/2)5.5.sin 45^o=25/(2sqrt2)##

The area of the octagon = ##8(25/(2sqrt2))=25sqrt2##..