Find the area of the regular 20-gon with radius 9 mm.

The radius is equal to the side of the polygon. The 20-gon has 20 sides. 

let n = number of sides of the polygon
     A = area of the polygon
     s = measure of one side of the polygon
     a = apothem

a = s / (2tan(180/n))
a = 9mm / (2tan(180/20))
a = 28.41 mm

P = s * n
P = 9mm * 20
P = 180 mm

A = a * P / 2
A = 28.41 mm * 180 mm / 2
A = 2556.9 mm^2