Skip to content
Related Articles

Related Articles

Improve Article
Diagonal of a Regular Pentagon
  • Last Updated : 10 Mar, 2021

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 <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;
}

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




<?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
?>

Javascript




<script>
    // Javascript 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
        let d = 1.22 * a;
        return d;
    }
     
    let a = 6;
    document.write(pentdiagonal(a));
     
</script>
Output: 
7.32

 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer Geeks Classes Live




My Personal Notes arrow_drop_up
Recommended Articles
Page :