A polygon has 14 sides. How many triangles can be drawn using the vertices of…

Concept: When no three vertices of a polygon are collinear (as in a convex polygon), any 3 chosen vertices always form exactly one distinct triangle. So the number of triangles equals the number of ways to choose 3 vertices out of n, i.e. nC3 = n! / (3!(n-3)!).

1. Here n = 14 (the polygon has 14 vertices).

2. Apply the combination formula: 14C3 = (14 x 13 x 12) / (3 x 2 x 1).

3. Multiply the numerator: 14 x 13 x 12 = 2184.

4. Divide by 3! = 6: 2184 / 6 = 364.

Cross-check: 14 x 13 x 12 / 6 can also be simplified as 14 x 13 x 2 = 364, confirming the same result via a different grouping of the multiplication.