AHSME 1967 Problem 9

Let $K$, in square units, be the area of a trapezoid such that the shorter base, the altitude, and the longer base, in that order, are in arithmetic progression. Then: $\textbf{(A)}\ K \text{must be an integer} \textbf{(B)}\ K \text{must be a rational fraction} \\ \textbf{(C)}\ K \text{must be an irrational number} \textbf{(D)}\ K \text{must be an integer or a rational fraction}$ $\textbf{(E)}\ \text{taken alone neither} \textbf{(A)} \text{nor} \textbf{(B)} \text{nor} \textbf{(C)} \text{nor} \textbf{(D)} \text{is true}$