"Things You Wouldn't Know If We Didn't Blog Intermittently."
Woo, got it right!
It helps to draw a line from the center of the regular hexagon, bisecting the shaded region, and out to the edge of the hexagon. Doing so creates 6 identical small triangles that take up one sixth of the area of the hexagon, top left. So 2/6 times 1/6 = 2/36 = 1/18.