Are you sure you want to lay tile while you still have bare concrete basement walls? Ignoring utilities, the general sequence for finishing a basement is level the floor, build stud & drywall false walls along the face of any exterior = concrete walls, build interior walls and doorways as needed, install a ceiling, doors, windows, then paint the walls and ceiling, then install flooring, then finally install and paint trim.
If you’re putting down tile on a raw concrete floor and abutting raw concrete walls there’s typically a few steps in the middle you may be overlooking.
Actually, the walls are finished. We had to pull up the old carpet and decided to replace it with tile and area rugs. There are baseboards I can hide some mistakes with
And for the pedants, you’re correct, the room is a trapezoid. It’s been a long time since I learned shapes.
At this point, my biggest concern is that I’m going to end up with a bunch of narrow tile on one (or two) sides that look like a map of Idaho.
An inch in 10 feet is not a huge out-of-square. The big obstacle is just the fact the room is not an even number of feet in each direction. The small out-of-square is just the cherry on the obstacle sundae.
The big idea is that it’s bad to do the floor by starting from, say, the left edge then going towards the right using full tile after full tile so you end up with 10 full tiles plus a 1" to 2" strip tapering along the right edge. That’s definitely the wrong way.
Instead you want this. Set it up so you have a 6 to 6-1/2" strip tapering along the left edge of the room and a 7 to 7-1/2" strip tapering along the right edge of the room and 9 full-sized tiles sandwiched in between. The taper will be far less obvious and the half-sized tiles will look very ordinary.
The downside is you end up cutting twice as many tiles so there’s more work and more wastage. As said by the others above, you accomplish this goal by figuring out where the middle of the room is, adjusting left/right and up/down a little as needed to distribute the difference between full tiles and the actual room size more or less evenly, then laying tiles outwards from there.