Find number of diagonals in n sided convex polygon

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 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



Output :

5 sided convex polygon have 5 diagonals

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Improved By : Sam007, jit_t, 29AjayKumar

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