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