Question

How Many Distinct Triangles Are Formed in an N-Gon?

A) n * (n-1) * (n-2) / 6
B) n * (n-1) / 2
C) n
D) n²

Answer 1

The number of distinct triangles formed in an n-gon is given by the formula n * (n-1) * (n-2) / 6.

Step-by-step explanation:

The number of distinct triangles formed in an n-gon is given by the formula n * (n-1) * (n-2) / 6. This formula can be derived by counting the number of ways to select three points from the n vertices of the n-gon. Let's break down the formula:

1. n represents the number of vertices in the n-gon.
2. n-1 represents the number of ways to select the second vertex after selecting the first vertex.
3. n-2 represents the number of ways to select the third vertex after selecting the first two vertices.
4. Dividing by 6 accounts for the fact that each triangle is counted 6 times due to rotational symmetries.

Therefore, the correct answer is A) n * (n-1) * (n-2) / 6.