A steel wire, when bent in the form of a square, encloses an area of 121 cm². The same wire is bent in the form of a circle. Find area of the circle.

Given:

Area of the square = 121 cm²

Let s be the side of the square.

As we know, the area of the square = side²

⇒ s² = 121

⇒ s = $\sqrt{121}$

⇒ s = 11

Total length of the wire = Perimeter of the square

As we know, the perimeter of the square = 4 x side

= 4 x 11

= 44 cm

Perimeter of the square = Circumference of the circle

Let r be the radius of the circle.

⇒ 2πr = 44

$⇒ 2 \times \dfrac{22}{7} \times r = 44\\[1em] ⇒ \dfrac{44}{7} \times r = 44\\[1em] ⇒ r = \dfrac{7 \times 44}{44}\\[1em] ⇒ r = \dfrac{308}{44}\\[1em] ⇒ r = 7$

Area of the circle = πr²

$= \dfrac{22}{7} \times 7^2\\[1em] = \dfrac{22}{7} \times 49\\[1em] = \dfrac{1,078}{7}\\[1em] = 154$

Hence, the area of the circle is 154 cm².