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

Sum

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

#### Solution

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.

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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.6 | Q 11. (a) | Page 90