Question

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

Answer 1

P = 14.18 unit

Explanation:

`p = 2\pi * r \\ 4\pi = 2\pi * r \\ r = (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 = √(12.56) \\ x = 3.544 \: unit \\ p = 4x \\ p = 4(3.544) \\ p = 14.18 \: unit`

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Answer 2

• 8√π or 14.18 units

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