Find the number of diagonals of
(i) a hexagon,
(ii) a decagon,
(iii) a polygon of 18 sides
For a diagonal to be formed, 2 vertices are required. Thus in a polygon, there are 10 sides. And no. of lines can be formed are nC2, but in nC2 the sides are also included. N of them is sides.
Thus the no. of diagonals are nC2 - n
(i) hexagon
n=6
so no of diagonal is 6C2-6
= 9
(ii) decagon
n= 10
so no of diagonal is 10C2-10
= 35
(iii) N= 18
so no of diagonal is 18C2-18
= 135