Distinct points $P,Q,R,S$ lie on a line, with $PQ=1$, $QR=2$, and $RS=3$. Points $T,U,V$ lie on a second line, parallel to the first, with $TU=2$ and $UV=4$. A triangle with positive area has three of the seven points as its vertices. How many possible values are there for the area of the triangle?