How to find the area of a circle using the circumference?

The circumference of a circle(C) = 2πr (where r denotes the radius of the circle) is the total boundary of the circle

The area of a circle(A) = πr² is the total space occupied by a circle

Answer: The area of a circle = C²/4π, where 'C' is the circumference of the circle

Let us see how we arrive at this equation

Explanation:

C = 2πr 

⇒ C² = 4π²r²

⇒ C² = πr² × 4π = 4π × (A)

where, A = Area of the circle

⇒ Area of the circle(A) = C²/4π

Hence the area of the circle with circumference 'C' is C²/4π