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.

`#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; `
`} ` |

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`// 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 ` |

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`# 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 ` |

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`// 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 ` |

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`<?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 ` `?> ` |

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**Output :**

5 sided convex polygon have 5 diagonals

This article is contributed by **Pratik Chhajer**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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