how do you find the area of a polygon given its radius?

Anonymous's answer assumed the radius is the apothem, which is the radius of the maximum inscribed circle.

If the radius is that of the minimum circumscribed circle (imagine a circle completely surrounding the polygon and shrinking it until it just touches all the vertices, but doesn't cross to the inside of the polygon anywhere) then, assuming we have a regular polygon with n sides, chop the polygon into n equal triangles.  Find the area of each triangle from (1/2)base*height, where base = 2*radius*sin(180°/n) and height = radius*cos(180°/n).

So total area of polygon = n*radius²*sin(180°/n)*cos(180°/n) = (n/2)*radius²*sin(360°/n)

This is for a regular polygon. Which basically means that all the sides are equal and all the angles are equal within the polygon. The radius given is also called the apothem, if it extends from the center and bisects a side. Hopefully, it does in this case or my answer won't help you.

Luckily for you, you are given the value of your apothem and you don't need to go through the trouble of finding it. You need to multiply the apothem and the perimeter of your polygon. If you are not given a measurement for the side of your polygon, it can be found with the length of your apothem and the 90 degree angle formed when the apothem bisected that side. After multiplying, divide your answer by 2.