I know that why we take area of a rectangle proportional to the product of its width and height. I also know why take area proportional to product. It is due to the theorem of Joint Variation. But it's really hard for me to make a visual concept or make sense of that how product of width and height give us the area of a rectangle?
The area of a rectangle of sides $a$ and $b$ is defined to be $ab$. The motivation for this definition is coming from counting points in discrete rectangles. If you arrange $b$ rows of marbles, each row having $a$ marbles, then the total number of marbles you have in the rectangle is $ab$.