# 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

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 <iostream>` `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

`<?php` `// PHP function to find number` `// of diagonals in n sided` `// convex polygon` `function` `numberOfDiagonals(` `$n` `)` `{` ` ` `return` `$n` `* (` `$n` `- 3) / 2;` `}` `// Driver Code` `$n` `= 5;` `echo` `$n` `, ` `" sided convex polygon have "` `;` `echo` `numberOfDiagonals(` `$n` `) ,` ` ` `" diagonals"` `;` ` ` `// This code is contributed by aj_36` `?>` |

## Javascript

`<script>` `// Javascript function to find number of` `// diagonals in n sided convex polygon` `function` `numberOfDiagonals(n)` `{` ` ` `return` `n * (n - 3) / 2;` `}` `// Driver code` `var` `n = 5;` `document.write(n + ` `" sided convex polygon have "` `);` `document.write(numberOfDiagonals(n) + ` `" diagonals"` `);` `// This code is contributed by Ankita saini` `</script>` |

**Output :**

5 sided convex polygon have 5 diagonals

**Time Complexity:** O(1)

**Auxiliary Space: **O(1)

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