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Find number of diagonals in n sided convex polygon
  • Difficulty Level : Medium
  • Last Updated : 13 Apr, 2021

Given n > 3, find number of diagonals in n sided convex polygon.
According to Wikipedia, In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal.

Examples : 

Input : 5
Output : 5

Explanation: Five possible diagonals are : AC, AD, BD, BE, CE 
 

 



Solution :

Since for an n-sided convex polygon, from each vertex, we can draw n-3 diagonals leaving two adjacent vertices and itself. Following this way for n-vertices, there will be n*(n-3) diagonals but then we will be calculating each diagonal twice so total number of diagonals become n*(n-3)/2
Here is code for above formula.

C++




#include <iostream>
using namespace std;
 
// C++ function to find number of diagonals
// in n sided convex polygon
int numberOfDiagonals(int n)
{
    return n * (n - 3) / 2;
}
 
// driver code to test above function
int main()
{
    int n = 5;
    cout << n << " sided convex polygon have ";
    cout << numberOfDiagonals(n) << " diagonals";
    return 0;
}

Java




// Java function to find number of diagonals
// in n sided convex polygon
 
public class Diagonals {
 
    static int numberOfDiagonals(int n)
    {
        return n * (n - 3) / 2;
    }
 
    // driver code to test above function
    public static void main(String[] args)
    {
        int n = 5;
        System.out.print(n + " sided convex polygon have ");
        System.out.println(numberOfDiagonals(n) + " diagonals");
    }
}
 
// This code is contributed by Saket Kumar

Python3




# Python3 program to find number of diagonals
# in n sided convex polygon
def numberOfDiagonals(n):
    return n * (n - 3) / 2
 
  
# driver code to test above function
def main():
    n = 5
    print(n , " sided convex polygon have ")
    print(numberOfDiagonals(n) , " diagonals")
 
if __name__ == '__main__':
    main()
 
#this code contributed by 29AjayKumar

C#




// C# function to find number of diagonals
// in n sided convex polygon
using System;
 
class GFG {
     
    static int numberOfDiagonals(int n)
    {
        return n * (n - 3) / 2;
    }
 
    // driver code to test above function
    public static void Main()
    {
        int n = 5;
        Console.Write(n + " sided convex polygon have ");
         
        Console.WriteLine(numberOfDiagonals(n) +
                                  " diagonals");
    }
}
 
// This code is contributed by Sam007

PHP




<?php
// PHP function to find number
// of diagonals in n sided
// convex polygon
function numberOfDiagonals($n)
{
    return $n * ($n - 3) / 2;
}
 
// Driver Code
$n = 5;
echo $n , " sided convex polygon have ";
echo numberOfDiagonals($n) ,
               " diagonals";
     
// This code is contributed by aj_36
?>

Javascript




<script>
 
// Javascript function to find number of
// diagonals in n sided convex polygon
function numberOfDiagonals(n)
{
    return n * (n - 3) / 2;
}
 
// Driver code
var n = 5;
document.write(n + " sided convex polygon have ");
document.write(numberOfDiagonals(n) + " diagonals");
 
// This code is contributed by Ankita saini
 
</script>

Output :

5 sided convex polygon have 5 diagonals

This article is contributed by Pratik Chhajer. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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