Question

Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 15

Answer 1

There are n vertices in the polygon of n-sides.

If we join any two vertices, we get either side or the diagonal of the polygon.

Two vertices can be joined in ⁿC₂ ways.

∴ total number of sides and diagonals = ⁿC₂ 

But there are n sides in the polygon.

∴ total number of the diagonals = ⁿC₂ – n

n = 15 sides

∴ the number of diagonal that can be drawn

= ¹⁵C₂ – 15

=`(15!)/(2!13!) - 15`

= `(15 xx 14 xx 13!)/(2 xx 13!) - 15`

= `(15 xx 14)/2 - 15`

= 105 – 15

= 90