How many times area is of perimeter how to find area when perimeter is given?

Given: Perimeter.

To do: To establish relationship between Perimeter and Area. And to know that how to find the area if perimeter is given.

Solution: 

$( i)$To find the area of a square when its perimeter is given.

Let there is a square. And "$a$" is its side.

Then, perimeter of the square, $s=a+a+a+a=4a$

$\Rightarrow a=\frac{s}{4}$

And its also known that area of a square, $A=side\times side=a\times a=a^{2}$

$\Rightarrow A=( \frac{s}{4})^{2}$

$\Rightarrow A=\frac{s^{2}}{16}$

$\boxed{ Hence, If\ perimeter\ of\ a square is "$s$", then\ the\ area\ of\ the\ square, A=\frac{s^{2}}{16}}$

$( ii)$. To find the area of a circle if its perimeter is given.

Let there is a circle with radius "$r$".

As known its perimeter$( circumference), s=2\pi r$

$\Rightarrow r=\frac{s}{2\pi}$

As Known, area of the circle $A= \pi r^{2}$

$\Rightarrow A=\pi\times(\frac{s}{2\pi})^{2}$

$\boxed{Hence,\ The\ area\ of\ a\ circle\ A=\pi\times(\frac{s}{2\pi})^{2},  "s" is\ perimeter\ of\ the\ circle.}$

Now, To find the area of the of a rectangle when only perimeter is given , is not possible.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

18 Views

Kickstart Your Career

Get certified by completing the course

Get Started