Olympiad Geometry · Superchallenge problem

A square is drawn so that the lines containing its four sides pass through the points $P(0, 0)$, $Q(5, 1)$, $R(4, 6)$, and $S(1, 8)$, one point on each line, going around the square in that order (so $P$ and $R$ are on the lines of opposite sides). Find the largest possible area of the square.