If the length and width of a rectangle each doubled what happens to the area of the rectangle

It would quadruple.

Basically, it will quadruple because you are multiplying, which doesn't make much sense actually.

An example is with a 2 by 2 figure, you would get 4 squared as the area, but if you double both sides, 4 by 4, you would get 16 squared as the area.