What is the area of a regular 15-gon with a radius of 5mm

(assuming the radius is the inradius (or the apothem))

To get the side length, we use this formula:

side length = apothem * (2 * tan (180/15))

side length = 5 * 2 * 0.21256

side length = 2.1256

Polygon Area = (# of sides * side length * apothem) / 2

Polygon Area = (15 * 2.1256 * 5) / 2

Polygon Area = 79.71