Question

Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 12

Answer 1

In an n-sided polygon, there are ‘n’ points and ‘n’ sides.

∴ Through ‘n’ points we can draw ⁿC₂ lines including sides.

∴ Number of diagonals in n sided polygon

= ⁿC₂ – n   ...(n = number of sides)

n = 12, ⁿC₂ – n  = ¹²C₂ – 12

= `(12 xx 11)/(1 xx 2) - 12`

= 66 – 12

= 54