Question

Find the number of triangles which can be formed by joining the angular points of a

polygon of 8 sides as vertices.​

Answer 1

Answer:

56

Step-by-step explanation:

triangle needs 3 points.

And polygon of 8 sides has 8 angular points.

Hence, number of triangle formed,

=8C3=8×7×61×2×3=56

Answer 2

56 triangles.

A triangle has three vertices. The given polygon is has 8 sides one of which has to a vertex of the traingle to be drawn. Thus, this can be done by selecting a combination of any 3 sides out of the 8.

That is,

Number of triangles formed = 8C3

where nCr = $\frac{n!}{r!*(n-r)!}$

∴ Number of triangles formed = $\frac{8!}{3!*(8-3)!}$

∴ Number of triangles formed = $\frac{8!}{3!*5!}$

∴ Number of triangles formed = $\frac{8*7*6}{3*2*1}$

∴ Number of triangles formed = 8*7

∴ Number of triangles formed = 56.