Question

Consider a regular polygon with 10 sides. What is the number of triangles that can be formed by joining the vertices which have no common side with any of the sides of the polygon?
1. 25
2. 50
3. 75
4. 100

Answer 1

Correct Answer - Option 2 : 50

Formula used:

Triangle having no side common with those of the polygon = 

\(\rm \frac{n(n-4)(n-5)}{6}\)

n is the sides of the polygon.

Calculation:

Here n = 10

Triangle having no side common with those of the polygon

= \(\rm \frac{10(10-4)(10-5)}{6}\)

= \(\rm \frac{10\times 6\times 5}{6}\)

= 50

∴ The number of triangles is 50.