What is the formula to find area using circumference?

Answer 1

Area = pi x r squared

In other words, pi times the (radius squared)

Your answer gives the area using radius. The question asked for area using circumference.

Here are the formulas:

circumference = 2 X pi X r

area = pi X r2

Square both side of the first equation.

circumference2 = 4 X pi2 X r2

Then solve for r2.

r2 = circumference2/4pi2

Substitute circumference2/4pi2 for r2 in the second equation.

area = pi X circumference2/4pi2

Simplify.

area = circumference2 / 4pi

Let's test the formula using an example

Consider a circle of diameter 10 ft.

Circumference is 2 X pi X r

r = 1/2 X diameter

Circumference = 2 X 3.1416 X 5 = 31.416 ft

Area = pi X r2

Area = 3.1416 X 52 = 78.54 sq ft

Area determined from circumference:

Area = circumference2 / 4pi

Area = 31.4162 / 4 X 3.1416 = 78.54 ft

78.54 ft was the answer calculated for area using either radius or circumference; so the formula checks out.