Unclassified (maths): JEE Advanced 2020 Mathematics question

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