I know not all shapes satisfy this relationship, but what is your intuition behind this formula that finds area (base*height=area). I think it would be best if we focus just on rectangles and squares since they seem to be the most elementary case. I can think of a proof dealing with integer numbers, but it blows my mind how one can generalise this equation to include the irrational numbers. In other math forums they told it was just regarded as an axiom, but I'm pretty sure there must be a rigorous proof out there. How do you prove this? I was asked what my level was so I'll say it here: I've seen nothing beyond multivariable calculus. Thanks a lot.