I've used the diagonally-pieced backing technique referenced above several times successfully. I really like it. Here is an easy-to-use calculator from Jinny Beyer. Download it and it will make the calculations for you.
https://jinnybeyer.com/wp-content/up...-Worksheet.pdf
Watson, I made some assumptions about your situation, I *think* you might have enough fabric for a diagonal backing. I filled out the form and said you wanted the backing to be 55 x 55, and that your chosen fabric is 44" wide. It says you need 2.04 yards.