NIELIT 2016 MAR Scientist B - Section B: 1

Question

The number of ways to cut a six sided convex polygon whose vertices are labeled into four triangles using diagonal lines that do not cross is

• A. $13$
• B. $14$
• C. $12$
• D. $11$

Answer 1

option B is correct. Let us take the vertices as A,B,C,D,E,and F. From A if we draw diagonals we get totaly new 4 triangles. From B also we get 4 new triangles, from C we get 3 new triangles and  D we get thre new triangles but from E and F we donot get any new triangles because we have already obtained the same while drawing diagonals from A,B,C,D .

Hence The Total Triangles Are 14 and the option B is correct.

Answer 2

Option (B) 14

source : https://www.geeksforgeeks.org/number-of-ways-a-convex-polygon-of-n2-sides-can-split-into-triangles-by-connecting-vertices/