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?
A circle's circumference C is 2πr, where r is the radius. The formula for the area of a circle A is πr^2.
Since the circumference of a circle is related to the radius by C = 2πr, we can rearrange this equation to solve for r: r = C/(2π).
Now, substituting r = C/(2π) into the formula for the area of a circle A = πr^2, we get:
A = π(C/(2π))^2 = π(C^2/(4π^2)) = C^2/(4π).
Therefore, the equation representing the area of a circle in terms of its circumference is A = C^2/(4π).