Adu and Amu have bought two pieces of land on the Moon from an e-store. Both the pieces of land have the same perimeters, but Adu’s piece of land is in the shape of a square, while Amu’s piece of land is in the shape of a circle.
The ratio of the areas of Adu’s piece of land to Amu’s piece of land is:

It is given that the perimeters of areas are equal for both of them. Let the equal perimeter be P.

Adu's piece is a square, and the perimeter of the square =  4s = P

Side of the square $$s=\ \dfrac{P}{4}$$

Amu's piece is a circle, and the perimeter of the circle = $$2\pi\ r=\ P$$

The radius of the circle $$r=\ \dfrac{P}{2\pi\ }$$

The ratio of areas is,

$$s^2\ :\ \pi\ r^2$$  $$=\left(\dfrac{P}{4}\right)^{^2}:\ \pi\ \left(\dfrac{P}{2\pi\ }\right)^{^2}$$ $$=\ \dfrac{P^2}{16}\ :\ \pi\times\dfrac{P^2}{4\pi^2\ }$$  $$=\ \dfrac{1}{4}\ :\ \dfrac{1}{\ \pi\ }\ =\ $$  $$\pi\ \ :\ \ 4$$

Hence, the correct answer is option D.