I want to rigorously prove the idea that Base*Height=Area works (I do realise there are shapes which do not satisfy this equation). I think I can see why it works for integer values, but I want something that gives me the correct intuition for all positive numbers.
Because of my level, I would appreciate if nothing beyond calculus is used to prove this. (Although I doubt calculus is needed).
Edit: As asked, my level is multivariable calculus, or CALC III in the US I guess. I want to prove this basically for a rectangle.
Thanks a lot.