Question

what is the perimeter of a square which has the same area as a circle with circumference of 4 pi

Answer 1

Answer:

P = 14.18 unit

Step-by-step explanation:

$p = 2\pi \times r \\ 4\pi = 2\pi \times r \\ r = \frac{4\pi}{2\pi} \\ r = 2 \: unit \\ \\ a = \pi {r}^{2} \\ a = (3.14) {(2)}^{2} \\ a = 12.56 \: {unit}^{2} \\ a(circle) = a(square) \\ a = {x}^{2} \\ 12.56 = {x}^{2} \\ x = \sqrt{12.56} \\ x = 3.544 \: unit \\ p = 4x \\ p = 4(3.544) \\ p = 14.18 \: unit$

I hope that is useful for you :)

Answer 2

Answer:

• 8√π  or 14.18 units

Step-by-step explanation:

Circumference of the circle:

• C = 2πr = 4π ⇒ r = 2

Area of the circle:

• A = πr² = π*2² = 4π

Area of the square, same as the area of the circle:

• a² = 4π

Side of the square:

• a = √4π = 2√π

Perimeter of the square:

• P = 4a = 4*2√π = 8√π  or 14.18 units