Answer:
1,302 triangles
Step-by-step explanation:
All triangles are formed by the intersection of three diagonals at three different points. There are five arrangements of three diagonals to consider. We classify them based on the number of distinct diagonal endpoints. We will directly count the number of triangles with 3, 4, and 5 endpoints. We will then count the number of potential triangles with 6 endpoints, then correct for the false triangles.
You can make 84 triangles with 3 diagonal endpoints, 504 triangles with 4 diagonal endpoints, 630 triangles with 5 diagonal endpoints, and 84 triangles with 6 diagonal endpoints. This adds up to be 1,302 triangles altogether.
