2009 AMC 10B Problem 12

Distinct points A, B, C, and D lie on a line, with AB=BC=CD=1. Points E and F lie on a second line, parallel to the first, with EF=1. A triangle with positive area has three of the six points as its vertices. How many possible values are there for the area of the triangle?

\text{(A) } 3 \qquad \text{(B) } 4 \qquad \text{(C) } 5 \qquad \text{(D) } 6 \qquad \text{(E) } 7

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.