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

Answer 1

The area of a circle with circumference 4π is given by the formula A = πr^2, where r is the radius of the circle. Since the circumference is 4π, we have 4π = 2πr --> r = 2.

Therefore, the area of the circle is A = π(2)^2 = 4π.

Since the area of a square is given by A = side^2, and we want the square to have the same area as the circle, we have side^2 = 4π. Hence, the side length of the square is √4π = 2√π.

The perimeter of a square is given by P = 4s, where s is the side length. Thus, the perimeter of the square is P = 4(2√π) = 8√π.