How do I find a formula for the area of a circle with a circumference c?

C = pi * d

C=2pi*r

(1/2)C=(1/2)(2pi*r)
(1/2)C=pi*r
(1/2)C*r = pi*r^2 =A

To find a formula for the area of a circle with a given circumference c, you can use the formula for the circumference of a circle:

c = 2πr,

where c represents the circumference and r represents the radius of the circle.

To find the radius, you can rearrange the formula:

r = c / (2π).

Once you have the radius, you can use the formula for the area of a circle:

A = πr^2

where A represents the area and r is the radius.

Substitute the value of the radius (c / (2π)) into the area formula to get:

A = π(c / (2π))^2

Simplify the expression:

A = π(c^2 / 4π^2)

Cancel out the π terms:

A = c^2 / (4π)

Therefore, the formula for the area of a circle with a given circumference c is A = c^2 / (4π).