# If circle and square having the same perimeter. which shape has a greater area?

$\begin{array}{l}\text{Given that, perimeter of square and circle are equal.}\\ \text{Let, side of square is }a\ \text{and radius of circle is }r.\\ \text{so,}\ Perimeter\ of\ square=4a\ \ \\ \ \ \ \ \ Perimeter\ of\ circle\ \ =2\pi r\\ \text{As given condition, }4a=2\pi r\\ \Rightarrow a=\frac{\pi r}{2}\\ \text{Now, we can find the ratio of area}\\ \frac{area\ of\ circle}{area\ of\ square}=\frac{\pi r^2}{a^2}=\frac{\pi r^2}{\left(\frac{\pi r}{2}\right)^2}=\frac{4}{\pi}\\ \text{We know that value of }\ \pi\ \text{is }3.14.\ \text{So,}\ \frac{4}{\pi}\ \text{greater than 1.}\\ \text{It shows that, }area\ of\ circle\ >\ area\ of\ square.\end{array}$

## Most Viewed Questions

### Preparation Products

##### Knockout NEET May 2023 (Easy Installments)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 5499/-
##### Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
##### Knockout NEET Aug 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
##### Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-