2006 Fermat Problem 19

In the diagram, \triangle ABC is right-angled. Side AB is extended in each direction to points D and G such that DA = AB = BG. Similarly, BC is extended to points F and K so that FB = BC = CK, and AC is extended to points E and H so that EA = AC = CH. The ratio of the area of the hexagon DEFGHK to the area of \triangle ABC is

\textbf{(A)}\ 4:1\quad \textbf{(B)}\ 7:1\quad \textbf{(C)}\ 9:1\quad \textbf{(D)}\ 16:1\quad \textbf{(E)}\ 13:1

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 Fermat contests here.