What is the perimeter of a square which has the same area as a circle with circumference of 4π?

Answer 1

A = pi * r^2
A = 3.14 * 2^2
A = 12.56

√12.56 = 3.544

3.544 * 4 = perimeter

Answer 2

c = 2πr = 4π
so, r=2
a = πr^2 = 4π
A square with area 4π has side √(4π) = 2√π

So, its perimeter is 4*2√π = 8√π

Note that 8√π > 4π. A circle has minimum perimeter for a given area. Or, a circle has maximum area for a given perimeter.