A circle can be cut into smaller and smaller slices and rearranged in the shape of a parallelogram as shown.

The formula for finding the area, A, of a parallelogram with base b and height h is shown. Which equation represents the area of a circle in terms of its circumference?

1 answer

The formula for finding the area of a circle is A = πr^2, where r is the radius of the circle.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.

To find the area of a circle in terms of its circumference, we can rearrange the formula for the circumference to solve for r:

r = C / (2π)

Substitute this value of r into the formula for the area of a circle:

A = π(C / (2π))^2
A = π(C^2 / (4π^2))
A = C^2 / (4π)

Therefore, the equation representing the area of a circle in terms of its circumference is A = C^2 / (4π).