One of the problems with giving yardage for backings is that there are so many factors in determining how much you need. If you're sending the quilt out to a longarmer, you may need as much as 4" extra all around. You may want to ensure that the seam goes across the quilt horizontally. You may be able to find a wide backing. You may want to keep costs down by using the diagonal seam method, or by doing more piecing of the backing (resulting in seams that go in more than one direction). You may prefer not to have a seam right down the center. With all those issues, giving a formula that always works for backing is impossible.
3 1/2 yards may be enough for your quilt, if you are quilting it yourself. If you are sending it out to a longarmer it may not be enough.