I found this question recently in my booklet on hyperbolic geometry asking a very simple question but I could not answer it:
Why can we not define the area of a hyperbolic triangle as in the plane as half the product of the perpendicular and the base?
I know the half plane model and the Poincare disk models but I cannot find a satisfactory explanation. I thought it might have something to do with that there are no rectangles in hyperbolic geometry but I cannot proceed. Help appreciated.