Question

How many triangles, in terms of n, can be formed from the diagonals and sides of an n-sided polygon

Answer 1

The total number of triangles formed by joining the vertices of n-sided polygon is $\dfrac{n(n-1)(n-2)}{6}.$

Step-by-step explanation:

To find, the total number of triangles =

We know that,

Total number of triangles formed by joining the vertices of n-sided polygon

$=\dfrac{n(n-1)(n-2)}{6}$

Where, n is greater or equal to 3 (n ≥ 3)

Thus, the total number of triangles formed by joining the vertices of n-sided polygon is $\dfrac{n(n-1)(n-2)}{6}.$