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.