This is what I came up with. The measurements for the baby blanket are 30" for the small square and 40" for the larger one. This makes about a 2" border, which I think would also work for a placemat. My placemats measure 19 X 13, so subtract the 2" border, and you get 15 X 9, add in 1" for seam allowance (1/2" seams) so your center would be cut 16 X 10, and the backing/border piece would be 26 X 20. then just follow the tutorial.
Please, please, please get 2 pieces of scrap/ ugly fabric and make a practice one to see if I have calculated this right before you cut your good fabric!