2010 AIME II Problem 9

Let A B C D E F be a regular hexagon. Let G, H, I, J, K, and L be the midpoints of sides
A B, B C, C D, D E, E F, and A F, respectively. The segments A H, B I, C J, D K, E L,
and F G bound a smaller regular hexagon. Let the ratio of the area of the smaller hexagon to the area
of A B C D E F be expressed as a fraction \frac{m}{n} where m and n are relatively prime positive integers. Find m+n.