I'm going through serge Lang's Basic Mathematics in order to prepare for university mathematics. In section 7 on area and applications one must find the area of a region bounded by an ellipse.
$\frac{u^2}{6} + \frac{y^2}{3} = 1$
Most examples of how to solve this i've found require integration. but i know that the area of an ellipse is
$πab$
however the answer is
π$\sqrt{18}$
I'd like an example of the correct way to do so without using integration as the text is supposed to be a logically contained text on mathematics required for calculus, not calculus itself. Or in other words could someone explain the reasoning as to why it's
$π\sqrt{18}$
and not just
$π18$
I know it's due to the $1^2$ not being distributed to the 6 or 3, but without better algebraic understanding I dont think i can necessarily discern exactly why.