If the length of the diagonal of a square is increasing at the rate of $0.1 cm/sec.$ What is the rate of increase of its area when the side is $\large\frac{15}{\sqrt{2}} $cm?

Question

\[\begin{array}{1 1}(1)1.5 cm^{2}/sec&(2)\frac{1}{2\pi}\\(3)4\pi&(4)\frac{\pi}{3}\end{array}\]