Using my calculations you need at least 5 yards of fabric. When I calculate for a backing I use 40"s wide for the fabric standard. I count 1 fabric width till I exceed the width of the top. You would want to add an extra width if they would not give you any extra off the edges. Your quilt would be two. I than convert the length to yards, you have 2 yards. Multiply the number of widths needed by the length yardage and add one.
This gives you enough fabric to extend off each side for quilting and to allow for the shrinkage caused by the quilting.
You can piece your back together, be sure to allow for the seam allowance. And as a suggestion, I use at least a 1/2" seam allowance pressed open for backing.
This has always worked for me. Just a thought.