Welcome! Fortunately, backing gives you wiggle room. Depending on how you are going to quilt it, the backing should be 2 to 4 inches longer on all sides possibly more if you are sending it out (so 4 to 8" longer & wider).
Your cutting mat is not the best for measurement as it can warp. A quality yardstick or tape measure should measure the same, however. I would go with your tape.