Problem 42789. Regular polygon bounded by and bounding a circle

As the number of sides (or vertices) of a regular polygon goes to infinity, its perimeter and area go to the perimeter and area of the circle bounding it, while the radius of the circle bounded by the polygon goes to the radius of the bounding circle.

Given the radius of the bounding circle, R, and the number of sides of a regular polygon, n, return the polygon's perimeter, p, and area, a, as well as the radius of the circle bounded by it, r.

Note: n will always be an integer greater than 2. R will always be a real number greater than zero.

Example (square):

R = 1

n = 4

p = 5.6568

a = 2

r = 0.7071