- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
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.