Question

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

Answer 1

The circumference of a circle is given by: 2πr, where r is the radius of the circle. Equating 4π, we have 2πr = 4π so the radius of the circle is: r = 4/2 = 2. Then, the area of the circle is given by πr ^ 2 = π * (2 ^ 2) = 4π.Since the square and the circle have the same area, then: Let L be the side of the square, we have:  L ^ 2 = 4π, clearing L = 2 * (π ^ (1/2))The perimeter of a square is the sum of its sides:  P = L + L + L + L = 2 * (π ^ (1/2)) + 2 * (π ^ (1/2)) + 2 * (π ^ (1/2)) + 2 * (π) ^ (1/2))  P = 8 * (π ^ (1/2))