Question

Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 8

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 = 8 sides

∴ the number of diagonals that can be drawn

= ⁸C₂ – 8

= `(8!)/(2!6!) - 8`

= `(8 xx 7 xx 6!)/(2 xx 6!) - 8`

= 28 – 8

= 20