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?

1 Answer

#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)#