Answer:
Most people know the following two equations for a circle:
c = 2πr
a = πr2
What you can do then, is rearrange the latter of the two, solving for r, and then plug it into the first one where r currently is:
a = πr2
r2 = a/π
r = (a/π)1/2
Now that we have an equation for radius with respect to area, we can simply plug that into our equation for circumference:
c = 2πr
c = 2π(a/π)1/2
c = 2(π2)1/2(a/π)1/2
c = 2(π2a/π)1/2
c = 2(πa)1/2
Giving us the final answer. The circumference of a circle is equal to twice the square root of the product of pi and it's area.