# Diagonal of a Regular Pentagon

• Last Updated : 25 Jun, 2022

Given an integer a which is the side of a regular pentagon, the task is to find and print the length of its diagonal. Examples:

Input: a = 6
Output: 7.32
Input: a = 9
Output: 10.98

Approach: We know that the sum of interior angles of a polygon = (n – 2) * 180 where, n is the no. of sides in the polygon.
So, sum of interior angles of pentagon = 3 * 180 = 540 and each interior angle will be 108
Now, we have to find BC = 2 * x. If we draw a perpendicular AO on BC, we will see that the perpendicular bisects BC in BO and OC, as triangles AOB and AOC are congruent to each other.
So, in triangle AOB, sin(54) = x / a i.e. x = 0.61 * a
Therefore, diagonal length will be 2 * x i.e. 1.22 * a.
Below is the implementation of the above approach:

## C++

 `// C++ Program to find the diagonal``// of a regular pentagon``#include ``using` `namespace` `std;` `// Function to find the diagonal``// of a regular pentagon``float` `pentdiagonal(``float` `a)``{` `    ``// Side cannot be negative``    ``if` `(a < 0)``        ``return` `-1;` `    ``// Length of the diagonal``    ``float` `d = 1.22 * a;``    ``return` `d;``}` `// Driver code``int` `main()``{``    ``float` `a = 6;``    ``cout << pentdiagonal(a) << endl;``    ``return` `0;``}`

## Java

 `// Java Program to find the diagonal``// of a regular pentagon``class` `GFG``{``    ` `// Function to find the diagonal``// of a regular pentagon``static` `double` `pentdiagonal(``double` `a)``{` `    ``// Side cannot be negative``    ``if` `(a < ``0``)``        ``return` `-``1``;` `    ``// Length of the diagonal``    ``double` `d = ``1.22` `* a;``    ``return` `d;``}` `// Driver code``static` `public` `void` `main (String args[])``{``    ``double` `a = ``6``;``    ``System.out.println(pentdiagonal(a));``}``}` `// This code is contributed``// by Akanksha Rai`

## Python3

 `# Python3 Program to find the diagonal``# of a regular pentagon` `# Function to find the diagonal``# of a regular pentagon``def` `pentdiagonal(a) :` `    ``# Side cannot be negative``    ``if` `(a < ``0``) :``        ``return` `-``1` `    ``# Length of the diagonal``    ``d ``=` `1.22` `*` `a``    ``return` `d` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:` `    ``a ``=` `6``    ``print``(pentdiagonal(a))` `# This code is contributed by Ryuga`

## C#

 `// C# Program to find the diagonal``// of a regular pentagon``using` `System;` `public` `class` `GFG{``    ` `// Function to find the diagonal``// of a regular pentagon``static` `double` `pentdiagonal(``double` `a)``{` `    ``// Side cannot be negative``    ``if` `(a < 0)``        ``return` `-1;` `    ``// Length of the diagonal``    ``double` `d = 1.22 * a;``    ``return` `d;``}` `// Driver code``    ``static` `public` `void` `Main (){``    ``double` `a = 6;``    ``Console.WriteLine(pentdiagonal(a));``    ``}``}`

## PHP

 ``

## Javascript

 ``

Output:

`7.32`

Time Complexity: O(1)

Auxiliary Space: O(1)

My Personal Notes arrow_drop_up