# 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 <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
```

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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