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

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