Find the number of diagonals of
(i)a hexagon,
(ii)a decagon,
(iii)a polygon of 18 sides

Answer : 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

Hexagon N = 6

so no of diagonal is ⁶C2-6

= 9

• decagon N = 10

So no of diagonal is ¹⁰C2-10

= 35

• N= 18

So no of diagonal is ¹⁸C2-18

= 135