# Find the area of a circle if its circumference is equal to the perimeter of a rectangle with sides 6.28m and 12.56m.

August 22, 2021 | education

| Let’s find what the perimeter of this rectangle is.

According to the condition of the problem, the lengths of the sides of this rectangle are 6.28 m and 12.56 m, therefore, the perimeter P of this rectangle is:

P = 2 * (6.28 + 12.56) = 2 * 18.84 = 37.68 m.

According to the condition of the problem, the circumference is equal to the perimeter of this rectangle, therefore, the circumference is also 37.68 m.

Find the radius r of this circle:

r = 37.68 / (2π) = 18.84 / π m.

Find the area of the circle:

π * r ^ 2 = π * (18.84 / π) ^ 2 = 354.9456 / π m ^ 2.

Answer: the area of a circle is 354.9456 / π m ^ 2.

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