Question

The wire bent in the form of a square encloses an area of 484 sq.Cm. If the same wire is bent so as to form a circle than the area enclosed will be

Answer 1

this done by the fact that the perimeter of the square will be equal to the perimeter of the circle as the total length of the wire is 88cm

Answer 2

Let each side of a square be x cm and radius of the circle be r cm

Area of the square = $\sf{{484cm}^{2}}$

$\therefore$ $\sf{ {x}^{2} = 484 = x = 22cm}$

$\therefore$ Perimeter of the square

= 22 × 4 = 88cm = Length of the wire

= Circumference of the circle, when the same wire is bent in the form of a circle

= 2πr = 88

= $\sf{r=\frac{44}{π}}$

$\therefore$ Area of the circle =

= $\sf{\pi \times \frac{44}{\pi} \times \frac{44}{\pi} = \frac{44}{22} \times 7 \times 44}$

= $\sf{ {616cm}^{2}}$