While this may seem like a simple question, I have found it very difficult to answer.
My question is
"Why is the area of a rectangle given as $l\times h$?"
We define area as the "size of a two dimensional surface".
I can show with calculus and some geometry that a rectangle with some height $h$ and length $l$, the area of that rectangle is
$$\int_0^lhdx=l\times h$$
But I feel this is circular because we can't really define an integral until we know the area of a rectangle as being $l\times h$.
Using other geometric shapes is also circular because many of them come from either the area of a rectangle or the area of a triangle, which the area of triangle comes from the area of a rectangle!
Perhaps this could be one of those axioms or definitions, it could very well be the definition of area, but if not, could someone show, mathematically or in a proof that the area of a rectangle is given as $l\times h$?
