Between a square of perimeter 44 cm and a circle of circumference 44 cm, which figure has a larger area and by how much?

Correct option is D

​Given:
The perimeter of the square = 44 cm,
The circumference of the circle = 44 cm.

Formula Used:
Side of the square = $$\frac{\text{Perimeter of the square}}{4}$$​
Area of the square = $$\text{Side}^2$$​
Radius of the circle = $$\frac{\text{Circumference of the circle}}{2\pi}$$​
Area of the circle = $$\pi \times \text{Radius}^2$$​
Solution:
Side of the square:
Side = $$\frac{44}{4} = 11 \text{ cm}$$​
The area of the square is:
Area of the square = $$11^2 = 121 \text{ cm}^2$$​
Radius of the circle:
Radius = $$\frac{44}{2\pi} = \frac{44}{2 \times \frac{22}{7}} = 7 \text{ cm}$$​
The area of the circle is:
Area of the circle = $$\pi \times 7^2 = \frac{22}{7} \times 49 = 154 \text{ cm}^2$$​
Difference in area = 154 - 121 = $$33 \text{ cm}^2$$​
Thus, the circle has a larger area by 33 $$\text{ cm}^2$$​.

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