2003 Fermat Problem 22

Pentagon ABCDE is such that all five diagonals AC, BD, CE, DA, and EB lie entirely within the pentagon. If the area of each of the triangles ABC, BCD, CDE, DEA, and EAB is equal to 1, the area of the pentagon ABCDE is closest to

\textbf{(A)}\ 3.62\quad \textbf{(B)}\ 3.64\quad \textbf{(C)}\ 3.66\quad \textbf{(D)}\ 3.68\quad \textbf{(E)}\ 3.70

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