You know the experation for the area of a circle of radius R. It is Pi*R2.
But what about the formula for the area of an ellipse of semi-minor axis of length A and semi-major axis of length B? (These semi-major axes are half the lengths of, respectively, the smallest and largest diameters of the ellipse)
For example, the following is a standard formula for such an ellipse centered at the origin:
(x2/A2) + (y2/B2) = 1.
The area of such an ellipse is
Area = Pi * A * B ,
a very natural generalization of the formula for a circle!