I know he is an engineer but there is an easier way to figure the amount of fabric.
I decided how wide the back needed to be and subtracted the width of the fabric (allowing for selvages and seams) from what I needed.
I folded the fabric diagonally measured from the selvage edge the extra width plus seam allowances. Measure down from the top to that point. Then cut your fabric length that much extra long plus a fudge factor. After you cut the length, fold the piece diagonally and press the fold. After you cut the piece in half on the fold, lay it out putting the one piece up as much as needed to make your needed width. Sew the seam