Find the exact area of a circle having the given circumference.

4 (sqrt3 PI) ... ?

The solution to the problem is as follows:

since C = 2*pi*r = 4sqrt (3) * pi:

r = C/2*pi = 4sqrt (3) * pi / 2 * pi = 2sqrt (3)

Therefore, to solve for Area:

Area = pi*r^2 = pi * (2sqrt (3)) ^2 = 12pi

The area is 12pi.