# 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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