Diagonal of a Regular Pentagon

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++

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// C++ Program to find the diagonal
// of a regular pentagon
#include <bits/stdc++.h>
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;
}

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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 [tabby title = "Python3"]

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# 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 *
    return d
  
# Driver code 
if __name__ == "__main__" :
  
    a = 6
    print(pentdiagonal(a)) 
  
# This code is contributed by Ryuga

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C#

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// 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));
    }
}

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PHP

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<?php
// PHP Program to find the diagonal
// of a regular pentagon
  
// Function to find the diagonal 
// of a regular pentagon
function pentdiagonal($a)
{
  
    // Side cannot be negative
    if ($a < 0)
        return -1;
  
    // Length of the diagonal
    $d = 1.22 * $a;
    return $d;
}
  
// Driver code
$a = 6;
echo pentdiagonal($a);
  
// This code is contributed 
// by Sach_Code
?>

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Output:

7.32


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