Question

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

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 = 15
∴ The number of diagonals = ¹⁵C₂ – 15

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

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

= 105 – 15
= 90