Question

The perimeter of a circle and of a square are equal. If the perimeter of them is 44 cm then, the area of
which one is greater and how much?
​

Answer 1

$\purple{ \mathcal{ \large{ \boxed{Circle, \: 33 \: cm {}^{2} }}}}$

$\text{ \large{ \underline{ Given}}}$

• The perimeter of a circle and of a square are equal = 44 cm

$\text{ \underline{ \underline{ \large{To \: find}}}}$

• The area of which one is greater and how much?

$\huge{ \text{ \underline{ \underline{ \red{✿Solution}}}}}$

Perimeter of square = 44 cm

$\sf{ \therefore{4 × side = 44}} \\ \sf{ \orange{ = > side = 11 cm}} \\ \\ \sf{ \blue{Area \: of \: square = side {}^{2} }} \\ \sf{ \therefore{A = 11 {}^{2} } } \\ \sf{ \green{A = 121cm {}^{2} }}$

Perimeter of the circle = 44 cm

$\sf{ \therefore{2\pi \: r = 44cm}} \\ \sf{ = > 2 \times \frac{22}{7} \times r = 44} \\ \sf{ = > r = \frac{44 \times 7}{2 \times 22} } \\ \sf{ \orange{ = > r= 7cm}}$

$\sf{ \blue{Area \: of \: circle = \pi \: r {}^{2} }} \\ \sf{ \therefore{A = \frac{22}{7} \times {7}^{2} }} \\ \sf{ \green{ = > A= 154cm {}^{2} }}$

$\sf{ \underline{ \small{Hence \: area \: of \: circle \: is \: greater and \: (154 - 121) = 33 \: cm {}^{2} much \: greater}}}$

Hope this helps you!!