If the circumference of a circle is the same as the perimeter of the square with a side as 4 pi in, what is the area of the circle in square inches?

Answer 1

since c = 2πr, r = c/2π
since a circle has a = πr^2, a = π(c/2π)^2 = c^2/4π

the square has perimeter 4*4π = 16π

so, the circle has area

a = (16π)^2/4π = 64π