Start by drawing an isosceles right triangle The hypotenuse is the image of the beam and one of the legs is a diameter of the beam. That is, so c, the major axis of the ellipse, is . The minor axis is, of course, the diameter of the beam, D.

The area of an ellipse with major and minorsemi-axes a and b is so, yes, the area of this ellipse is , exactly what you have.