A regular decagon(12 sides) in inscribed in a circle with the radius r. The decagon has an area of108 in^2. What is the radius of the cirlce?

Answer 1

First of all a decagon has 10 sides, not 12.
Let's split it up into 10 isosceles triangles
Each triangle will have an area of 10.8 in^2 and a central angle of 36 degrees.
Area of triangle = (1/2)(r)(r)sin36
21.6 = r^2(sin36)
r^2 = 21.6/sin36
r = 3.56