Lets consider the points A (3,3), B(9,5), C(6,9), D(9,3), E(9,9) and F(3,9)
The area of the triangle ABC is given by the area of the square ADEF subtracted by the area of the triangles ADB, BEC and CFA.
The ADEF square has sides with length 6. Therefore, it's area is 6^2 = 36 square units.
The area of any triangle with base b and height h is (b*h)/2
For ADB triangle, we have b = 6 and h = 2, which implies (b*h)/2 = 6 square units
For BEC triangle, we have b = 3 and h = 4, which implies (b*h)/2 = 6 square units
And for CFA triangle, we have b = 3 and h = 6, which implies (b*h)/2 = 9 square units
Therefore, the area of ABC triangle is 36 - 6 - 6 - 9 = 15 square units