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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

=> pi*a^2/4*pi^2

=> a^2/4*pi

The area of the circle is a^2/4*pi square units

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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.

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