Let's see here ... a game board with area 160 in^2. We'll assume that the board is square. The area of a square is A = s^2, where s is the side length.
Re-writing that, we get s^2 = A, so that s = side length = approx. √(160 in^2),
or s = approx. 12.65 in. We are to round up to the nearest integer value, which wuld be 13 in.