In the given figure, $PQRS$ is a square of side $2 \: \mathrm{cm}$ and $PLMN$ is a rectangle. The corner $L$ of the rectangle is on the side $QR$. Side $MN$ of the rectangle passes through the corner $S$ of the square.
What is the area (in $\mathrm{cm}^{2}$ ) of the rectangle $PLMN$?
Note: The figure shown is representative.
- $2 \sqrt{2}$
- $2$
- $8$
- $4$
