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!