11" drum backing plates measure about 12 1/8" in diameter from lip to lip.
If I had to guess, I would say that backing plates for 10" drums probably measure ~11" in diameter.
If you have 11" drums, you have some additional work to do though. 11" drums came in 11x2", 11x2.5" and 11x3". The backing plates for each of those widths is different, and has to be matched to the correct width shoe and drum. If it turns out you have 11" brakes, let me know. I have backing plates for 11x2" and 11x2.5" brakes, so I may be able to figure out a way to measure them to tell the difference without the rest of the hardware.