What is the area of a circle if its circumferece is a?

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.