jmc

We begin with a diagram of the given information:

To increase the symmetry in the diagram, we can draw in the long diagonals of $ABCDEF$ as well as the mirror image of $△GHI$ across these diagonals:



These additional lines divide $ABCDEF$ into $24$ congruent equilateral triangles, of which $△GHI$ covers exactly $9$. Thus each of the triangles has area $\frac{225}{9}=25$, and hexagon $ABCDEF$ has area $24\cdot 25=\boxed{600}$.