Consider all rectangles lying in the region
$ \left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{R} \times \mathbb{R}: 0 \leq \mathrm{x} \leq \frac{\pi}{2} \text { and } 0 \leq \mathrm{y} \leq 2 \sin (2 \mathrm{x})\right\} $
and having one side on the $x$-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is