Question

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

Answer 1

Two points are needed to draw a segment.
A polygon of n sides has n vertices.
So, in a polygon of n sides, there will be
ⁿC₂ segments, which include its sides and diagonals both.
Since the polygon has n sides, the number of its diagonals is ⁿC₂ – n
Here, n = 12
∴ The number of diagonals = ¹²C₂ – 12

= `(12!)/((12 - 2)!2!) - 12`

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

= 66 – 12
= 54