jmc

The sides of the rectangle are parallel to the axes, so the fourth point must make a vertical line with (5,11) and a horizontal one with (16,-2); this means that the fourth point is (5,-2). The graph of the region inside the equation is a circle with radius 3 and center (5,-2): Since each angle of a rectangle is $90^{\circ }$ and the corner coincides with the center of the circle, the rectangle covers exactly a quarter of the circle. The area of the intersection is thus $\frac{1}{4}{r}^2\pi =\frac{1}{4}\cdot 3^2\pi =\boxed{\frac{9}{4}\pi }$.