Question

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

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 = 10
∴ The number of diagonals = ¹⁰C₂ – 10

= `(10!)/((10 - 2)!2!) - 10`

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

= 45 – 10
= 35.