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\\
(A) $\frac { 3 \pi } { 2 }$\\
(B) $\pi$\\
(C) $\frac { \pi } { 2 \sqrt { 3 } }$\\
(D) $\frac { \pi \sqrt { 3 } } { 2 }$