If area of a square is $44\, cm^2$, find the area of the circle formed by the same perimeter.

$56\, cm^2$

The correct answer is Option (3) → $56\, cm^2$

Area of square = $44 \text{ cm}^2$

$\text{Side of square} = \sqrt{44} = 2\sqrt{11}$

Perimeter of square:

$P = 4 \times 2\sqrt{11} = 8\sqrt{11}$​

This equals the circumference of the circle:

$2\pi r = 8\sqrt{11} \Rightarrow r = \frac{4\sqrt{11}}{\pi}$

Area of the circle:

$\pi r^2 = \pi \left(\frac{4\sqrt{11}}{\pi}\right)^2 = \frac{176}{\pi}$

Using $\pi \approx \frac{22}{7}$​:

$\frac{176}{\pi} \approx \frac{176 \times 7}{22} = 56$