If it wasn't superwash, I'd use size 9 needles and cast on 15 inches worth of stitches. Knit
enough rows to make it 15 inches the other way. Then toss the thing in the washing machine until it shrinks down and then stretch it into a square as needed.
I've actually made a hot pads that way as Christmas presents. I also make them a little over twice as long and fold them over and sew the sides to use as
oven mitts, but that's a bit more complicated.
With super wash, I'd go down a needle size to size 5 needles (so it's tighter/denser) and cast on however many stitches would make 10 inches. Keep knitting until it's a square, and then done! Since it's wool, it'll do a nice job of protecting the table from the hot pot/pan/teapot/etc.
If you want, I can pick up some of the same yarn and do a test hot pad. I can use the remaining wool for a hat or mitten for my kids.