1997 Pascal Problem 14

In the game "TRISQUARE", three points are awarded for each triangle found, and four points for each square. The highest number of points that can be achieved for the given diagram is

\textbf{(A)}\ 38\quad \textbf{(B)}\ 36\quad \textbf{(C)}\ 34\quad \textbf{(D)}\ 32\quad \textbf{(E)}\ 28

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.