To find the area of a rectangle, is it supposed to go area=lxw?

Yes. That's (length) times (width).

It doesn't make any difference if you multiply (width) times (length).
The result is the same.  That's one of the 'properties' of multiplication . . .
It doesn't matter which order you do it in.

Yes, the area of a rectangle is length times width (A=lw) or base times height (A=bh). They mean the same thing, just with different wording.

For example:
Let's say you have a rectangle with the following dimensions - 8 in. x 9 in.
Area = length * width
A = 8 * 9
A = 72
Therefore the area of this rectangle would be 72 square inches.