Question

The number of diagonals and triangles formed in an octagon are

• A. $20,56$
• B. $32,58$
• C. $30,58$
• D. $32,56$

Answer 1

Answer: (A)

$20,56$

Let $A_1,A_2,........,A_8$ be the vertices of the octagon.
One triangle is formed by selecting a group of 3 points from 8 given vertices.
No. of triangles = No. of groups of 3 each from 8 points = ${}^8{C}_3=\frac{\mathrm{8.7.6}}{6}=56$
(b) No. of lines that can be formed by using the given vertices of a polygon = No. of groups of 2 points each selected from the n points
=${}^8{C}_2=28$
Out of these 8 are the sides of the polygon and remaining$(28-8)$ are the diagonals = $20$
Hence, option 'A' is correct.