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

P = 2 * (a + b) – the formula for finding the perimeter of a rectangle, where a and b = are its width and length;
P = 2 * (6.28 + 12.56) = 2 * 18.84 = 37.68 (meters);
С = 2 * pi * R – the formula for finding the circumference, where pi = 3.14, R – the radius of the circle;
we know that С = P, then:
2 * pi * R = 37.68, which means R = 37.68 / (2 * pi) = 37.68 / 6.28 = 6 (meters);
S = pi * R ^ 2 – the formula for finding the area of a circle, then S = pi * 6 ^ 2 = 113.04 (square meters);
Answer: the area of the circle is 113.04 (m ^ 2).