Oh I just found the answer:
The two triangles that are shaded blue are similar.
So we have the following ratios:
3/3+9 = x/9
x=9/4
So height of the black triangle is 9 - 9/4 = 27/4
So area of black triangle is (9 * 27/4)/2 = 243/8
EDIT: here's the image
