Question

What will be the area of a circle whose perimeter is p?

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Answer 1

Step-by-step explanation:

Circumference of circle is 2πr=π

r=

2

1

Area of circle is πr

2

=π(

2

1

)

2

=

4

π

Answer 2

The area of the circle with the perimeter "p" is $p^{2} / (4\pi)$ or $0.08p^{2}$ square units.

The formulation of the Area and Perimeter of any circle with radius "r" is :

                $Perimeter = 2 * \pi * r\\ Area = \pi * r * r$

Step 1 : Calculating the radius of the circle :

Given the perimeter as "p", let us assume the radius of the circle to be "r". Then, according to the formula :

             $p = 2\pi *r\\r = p/(2\pi )$

Step 2: Calculating the area of the circle :

Given the perimeter as "p", and assumed radius "r". Then, according to the formula :

             $A = \pi r^{2}$

Using the value of "r" in terms of perimeter "p" found above :

            $A = \pi r^{2} \\\\A = \pi (p/2\pi )^{2} \\\\A = \pi * p^{2} / (4\pi ^{2}) \\\\A = p^{2} / (4\pi) \\\\A = 0.08p^{2}$

Hence, the area of the circle in terms of its perimeter "p" is $p^{2} / (4\pi)$ sq. units.

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