The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
0 votes
A polygon has 12 edges , How many diagonals does it have?

How to find the number of diagonals?
in Numerical Ability by (497 points) | 44 views

1 Answer

0 votes
For any $n$ side polygon, the number of diagonals are $\frac{n(n-3)}{2}$.

We can prove this as follows:

First, select a vertex from the polygon. This can be done in $n \choose 1$ ways.
To draw diagonals, we can choose any other vertex except the neighbouring vertices, giving us $n -1\choose 1$ ways.

This gives us a total of $n \times (n-3)$ diagonals.

However, we have overcounted by a factor of two here, since diagonal from $AB$ is same as diagonal from $BA$.

Hence, the total number of diagonals are $\frac{n(n-3)}{2}$
by Loyal (6.3k points)

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
49,830 questions
54,800 answers
80,731 users