A copper wire when bent in the form of a square encloses an area of 121 cm². If the same wire is bent into the form of a circle, find the area of the circle.

Area of square = (side)²

Given,

Area of square = 121 cm²

∴ (side)² = 121

⇒ (side)² = (11)²

⇒ side = 11 cm.

Perimeter of square = 4 × side = 4 × 11 = 44 cm.

Circumference of the circle of same wire = Perimeter of square of same wire

Let radius of circle formed = r cm.

∴ 2πr = 44

⇒ r = $\dfrac{44}{2π} = \dfrac{44}{2 \times \dfrac{22}{7}} = \dfrac{44 \times 7}{44}$

= 7 cm.

Area of circle = πr²

= $\dfrac{22}{7} \times (7)^2 = 22 \times 7$

= 154 cm².

Hence, area of circle = 154 cm².