Question

find the area of a regular pentagon inscribed in a circle whose equation is given by (x-4)^2 + (y+2)^2=25

Answer 1

The radius is √25=5 in this case.
find the area of each triangles first. (the pentagon can be divided into 5 isosceles triangles)
the two equal sides are 5 each, the angle between them is 360/5=72 degree, so the base side is 2*5*sin36, and the height is 5*Cos36
the area of each triangle is (1/2)*2*5*Sin36*5*Cos36
the total area of the 5 triangles is: 5*(1/2)*2*5*Sin36*5*Cos36
use a calculator: A≈59.44