Question

Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 10

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 = 10

ⁿC₂ – n = ¹⁰C₂ – 10

= `(10 xx 9)/(1 xx 2) - 10`

= 45 – 10

= 35