The formula for the area of an entire elippse is a*b*pi
where a and b are the lengths of the major and minor axes.
If you can find what the fractional amount of the whole ellipse that shaded region is......
That should be enough to get you going.
http://img253.imageshack.us/img253/8324/image002h.gif
How to find the area of a segment of an ellipse (shaded portion) with
respect to height?