The question given is, The figure shows a rectangle with two vertices on a semicircle of radius 2 and two vertices on the x-axis. Let $P(x, y)$ be the vertex that lies in the first quadrant.
(a) Express the area of rectangle as a function of $x$.
I am not getting how to deal with this problem. Area of rectangle is $A=xy$, I can substitute $\sqrt{4-x^{2}}$ in the place of $y$, to obtain $A=x\sqrt{4-x^{2}}$. But this does not complete the solution.
Please explain how to do this, I believe this may be a easiest question but I am not getting.
The graph is symmetric. You are missing a factor of 2.
The rectangle you have calculated is delimited by both axes, and has only one point on the semicircle. The rectangle required is two of these together, so your answer should be multiplied by 2.