What is the area of a hexagon with a radius of 18ft

Answer 1

Assume the hexagon is regular (all equal sides and interior angles)

Area = 1/2 * Apothem * Perimeter

You can use the radius to form a 30-60-90 right triangle, where the radius is the hypotenuse, the apothem is the leg opposite the 60 degree angle and half of the side of the hexagon is opposite the 30 degree angle.

Since the radius (hypotenuse) is 18, half the side opposite the 30 degree angle is 9 and the apothem is 9*sqrt(3).

Since half the side is 9, a full side is 18 and the perimeter is 6*18 = 108.

So area = 1/2 * 9 * sqrt(3) * 108 = 841.78