Question

What is the number of triangles that can be formed whose vertices are the vertices of an octagon but have only one side common with that of octagon?

• A. 16
• B. 3
• C. 48
• D. 64

Answer 1

The Correct Option is B

The number of triangles that can be formed with vertices of an octagon is given by choosing 3 vertices from 8. The total number of triangles is:

8C3 = 8 × 7 × 6 / 3 × 2 × 1 = 56.

However, the triangles with one side common with the octagon must include two adjacent vertices. There are 8 sides in the octagon, so there are 8 such triangles.

The total number of triangles with one side common with the octagon is: 56 −53 =3