Lower forty can also refer to the portion of one’s land that is closest to a river It has the advantage of being more fertile and better watered (unless it is so watered that it is just swamp) with the disadvantage of periodically being washed out or buried in (ultimately enriching) flood silt.
The last place I worked had a large expanse of mostly unused factory space (in the back, appropriately enough) that everyone referred to as “the back 40”.
It was better than calling it “the black hole” or “the big empty space”
I’ve always heard lower 40. It’s been a couple of c&w songs as well.
An ex used “time to mow the back 40” as “time to do something about my gross back hair”.