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

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.