If I have four dots, arranged in two rows of two to make a square, and I draw a triangle by joining three of the dots, there are four triangles I can draw, but they are all the same shape (they are congruent).

If I start with nine dots, arranged in three rows of three to make a square, how many different (non-congruent) triangles is it possible to draw?

What if I start with a square formed of sixteen dots? Or n² dots?