The circumference of a circle with radius r is 2*pi*r and the area of the circle is pi*r^2
For a circle with circumference a
2*pi*r = a
=> r = a / 2*pi
The area of the circle is pi*(a / 2*pi)^2
The area of the circle is a^2/4*pi square units
Given that a circumference of a circle is a.
We need to find the area of the circle as a function of a.
==> We know that:
C= 2*pi * r = a
==> r= a/2pi ..............(1)
Now we will determine the area of a circle formula.
==> A = r^2 * pi
But r= a/2pi
==> A = (a/2pi)^2 * pi
==> A = (a^2/4pi^2 * pi
==> A = (a^2/4pi )
Then the area of the circle is (a^2/4pi) square units.