By bending a wire, a square is made whose area is x sq. units. If a circle is made from the same wire, what will be its area?

Area of the square =x sq. units

Let the side be a
Area of the square =$a^2$=x
∴x=$a^2$  ....(i)

The perimeter of the square =4a units

If a circle is made with the same wire then its circumference is equal to the perimeter of the square.
Circumference of the circle =2πr

then,$$\begin{gathered} 2\mathrm{\pi r}=4\mathrm{a} \\ \mathrm{or}, \mathrm{\pi r}=2\mathrm{a} \\ \mathrm{or}, \mathrm{r}=\frac{2\mathrm{a}}{\mathrm{\pi }} \end{gathered}$$

The area of the circle =$\mathrm{\pi } {\mathrm{r}}^2$

$=\mathrm{\pi }{\left(\frac{2\mathrm{a}}{\mathrm{\pi }}\right)}^2$

=$\frac{4{\mathrm{a}}^2}{\mathrm{\pi }}$

$$\begin{gathered} =\frac{4a^2}{22}\times 7 \\ =\frac{14a^2}{11} \\ =\frac{14x}{11} \end{gathered}$$

Hence the area of the circle =$\frac{14x}{11} sq.units$