Best guess at reading as it is not giving me what I might like for measurements.
But I would be reasonably confident that it has enough to get it done but with caution. I always like to take great care when cutting blind as it is always possible to find wires that we don't expect.
But I did a bit of looking and sorting for info and maybe this will be what you need.
Click this drawing to make it easier to read but what I see is this.
You have a ceiling which is a sandwich of fiberglass outer and carpet laid directly on it inside. For support there are cross" "beams" at the points I marked in orange as well as tow short pieces where I would guess it is prepped for RV that have an option for a vent over the bed!
So that might make it "natural" to put one there, IF that is what you choose????
Some things I would want to think over are if that is the right place for me, I would want to think about how and where to tie into power. The cross brace is likely to be metal, making it somewhat hard to drill through to run power in the foam, etc you might find. So where to get the power?
My new favorite tool for cutting blind is an oscillating tool like this as it is so much safer and less prone to cutting things like wires that will wiggle enough to not be damaged.
This is one that is cheap for the one time user but I'm getting lots of use out of it.
https://www.walmart.com/ip/Hyper-Tou...Grit/730516237
Then I would go with cutting a 2X2 inch flap in the carpet, cut a hole in the ceiling and then run a stiff wire, etc. to feel if I find the metal in the places I "think" they are located. The idea of the flap is too allow for backing out and gluing the flap shut to cover the damage, if it all goes downhill! The idea is to feel around and make sure the braces allow me to fit the size vent in between the two and it not be 12 wide and I'm looking at needing 14!!!
Always nice to have a backup plan?