A regular octagon is placed in a unit circle such that each vertex lies on the circumference of the circle.
Find the perimeter of the octagon.
Using the Law of Cosines, we can find the side of the octagon, S, as
S^2 = 1^2 + 1^2 - 2 ( 1 * 1) cos (45°)
S^2 = 2 - [ 2 * √2 / 2 ]
S^2 = 2 - √2
S = √ [ 2 - √2 ] units
So....the perimeter is
8 √ [ 2 - √2 ] units ≈ 6.12 units
