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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 ``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

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## Javascript

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Output :

`5 sided convex polygon have 5 diagonals`

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