Find number of diagonals in n sided convex polygon (original) (raw)

Last Updated : 8 Aug, 2024

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

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 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

JavaScript

PHP

`

**Output :

5 sided convex polygon have 5 diagonals

**Time Complexity: O(1)

**Auxiliary Space: O(1)