Question

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

Answer 1

Answer:

perimeter = 8$\sqrt{\pi }$

Step-by-step explanation:

We require to calculate the area (A) of the circle

A = πr² ← r is the radius

circumference = 4π = 2πr, hence

2πr = 4π ( divide both sides by 2π )

r = 2, hence

A = π × 4 = 4π

The area of the square is therefore 4π and area = s² ← s is the side length

s² = 4π ( take the square root of both sides )

s = $\sqrt{4\pi }$ = 2$\sqrt{\pi }$, hence

perimeter = 4 × 2$\sqrt{\pi }$ = 8$\sqrt{\pi }$