The area of a square is $d$
We know that, if a square has $a$ units as the length of its side, then its area will be $a^2.$
$\Rightarrow \textbf{every side of the square will be } \sqrt{d}$
Now, the diagonal of the square will be $\sqrt{(\sqrt d)^2+(\sqrt d)^2} = \sqrt{2d}$
Now, $\sqrt{2d}$ is the perimeter of a circle.
∴ Radius of the circle will be $\dfrac{\sqrt{2d}}{2}$
We know $\color{black}{\textbf{Area of the circle}}$ is $\pi r^2$, where, $r = \text{radius of the circle}$
$ = \dfrac{22}{7} \times \dfrac{\sqrt{2d}}{2} \times \dfrac{\sqrt{2d}}{2}$
$= \dfrac{22}{7} \times \dfrac{2d}{2 \times 2} $
$= \dfrac{22}{7} \times \dfrac{d}{2}$
$=\color{Black}{ \pi . \dfrac{d}{2}}$
$\text{Option (D)}$