Number of triangles formed by joining vertices of n-sided polygon with one side common

Difficulty Level : Easy
Last Updated : 07 Apr, 2021

Given N-sided polygon we need to find the number of triangles formed by joining the vertices of the given polygon with exactly one side being common.
Examples:

Input : 6
Output : 12
The image below is of a triangle forming inside a Hexagon by joining vertices as shown above. The two triangles formed has one side (AB) common with that of a polygon.It depicts that with one edge of a hexagon we can make two triangles with one side common. We can’t take C or F as our third vertex as it will make 2 sides common with the hexagon.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.
In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.
Triangle with one side common of a hexagon
No of triangles formed ie equal to 12 as there are 6 edges in a hexagon.
Input : 5
Output : 5

Approach :

To make a triangle with one side common with a polygon the two vertices adjacent to the chosen common vertices cannot be considered as the third vertex of a triangle.
First select any one edge from the polygon. Consider this edge to be the common edge. Number of ways to select an edge in a polygon would be equal to n.
Now ,to form a triangle ,select any of the (n-4) vertices left .Two vertices of the common edge and two vertices adjacent to the common edge cannot be considered.
Number of triangle formed by joining the vertices of an n-sided polygon with one side common would be equal to n * ( n – 4) .

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above problem
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the number of triangles
void findTriangles(int n)
{
    int num;
    num = n * (n - 4);
 
    // print the number of triangles
    cout << num;
}
 
// Driver code
int main()
{
    // initialize the number of sides of a polygon
    int n;
    n = 6;
 
    findTriangles(n);
 
    return 0;
}

Java

// Java program to implement
// the above problem
class GFG
{
     
// Function to find the number of triangles
static void findTriangles(int n)
{
    int num;
    num = n * (n - 4);
 
    // print the number of triangles
    System.out.println(num);
}
 
// Driver code
public static void main(String [] args)
{
    // initialize the number of sides of a polygon
    int n;
    n = 6;
 
    findTriangles(n);
 
}
}
 
// This code is contributed by ihritik

Python3

# Python3 program to implement
# the above problem
 
# Function to find the number of triangles
def findTriangles(n):
    num = n * (n - 4)
 
    # print the number of triangles
    print(num)
 
# Driver code
# initialize the number of sides of a polygon
n = 6
 
findTriangles(n)
 
# This codee is contributed by mohit kumar 29

C#

// C# program to implement
// the above problem
using System;
 
class GFG
{
     
// Function to find the number of triangles
static void findTriangles(int n)
{
    int num;
    num = n * (n - 4);
 
    // print the number of triangles
    Console.WriteLine(num);
}
 
// Driver code
public static void Main()
{
    // initialize the number of sides of a polygon
    int n;
    n = 6;
 
    findTriangles(n);
 
}
}
 
// This code is contributed by ihritik

Javascript

<script>
 
// JavaScript program to implement
// the above problem
 
     
// Function to find the number of triangles
function findTriangles(n)
{
    var num;
    num = n * (n - 4);
 
    // print the number of triangles
    document.write(num);
}
 
// Driver code
 
// initialize the number of sides of a polygon
var n;
n = 6;
 
findTriangles(n);
 
 
// This code contributed by shikhasingrajput
 
</script>

Output:

Time Complexity: O(1)

My Personal Notes

Related Articles

Number of triangles formed by joining vertices of n-sided polygon with one side common

C++

Java

Python3

C#

Javascript