Length of the Diagonal of the Octagon

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Given here is a regular octagon of side length a, the task is to find the length of it’s diagonal.
Examples:

Input: a = 4
Output: 10.4525

Input: a = 5
Output: 13.0656

Approach: From the diagram it is clear that,

AB^2 + BC^2 = AC^2
here, in triangle AED,
b^2 + b^2 = a^2
or, b=a/?2(Please refer)
So, AB = a + 2b = a + ?2a
and, BC = a
So, diagonal AC = a?(4 + 2?2)

Below is the implementation of the above approach:

C++

// C++ Program to find the diagonal
// of the octagon
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the diagonal
// of the octagon
float octadiagonal(float a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // diagonal of the octagon
    return a * sqrt(4 + (2 * sqrt(2)));
}
 
// Driver code
int main()
{
    float a = 4;
    cout << octadiagonal(a) << endl;
 
    return 0;
}

Java

// Java  Program to find the diagonal 
// of the octagon 
import java.util.*;
class solution
{
   
// Function to find the diagonal 
// of the octagon 
static double octadiagonal(double a) 
{ 
   
    // side cannot be negative 
    if (a < 0) 
        return -1; 
   
    // diagonal of the octagon 
    return a * Math.sqrt(4 + (2 * Math.sqrt(2))); 
} 
   
// Driver code 
public static void main(String args[])
{ 
    double a = 4; 
    System.out.println( octadiagonal(a)); 
   
} 
}
//contributed by Arnab Kundu

Python3

# Python3 Program to find the diagonal
# of the octagon
import math
# Function to find the diagonal
# of the octagon
def octadiagonal(a):
 
    # side cannot be negative
    if (a < 0):
        return -1;
 
    # diagonal of the octagon
    return a * math.sqrt(4 + (2 * math.sqrt(2)))
 
 
# Driver code
if __name__=='__main__':
    a = 4
    print (octadiagonal(a))
 
# This code is contributed by 
# Shivi_Aggarwal 

C#

// C# Program to find the diagonal 
// of the octagon 
using System;
 
class GFG
{
 
// Function to find the diagonal 
// of the octagon 
static double octadiagonal(double a) 
{ 
 
    // side cannot be negative 
    if (a < 0) 
        return -1; 
 
    // diagonal of the octagon 
    return a * Math.Sqrt(4 + 
          (2 * Math.Sqrt(2))); 
} 
 
// Driver code 
public static void Main()
{ 
    double a = 4; 
    Console.WriteLine(octadiagonal(a)); 
} 
}
 
// This code is contributed 
// by inder_verma

PHP

<?php
// PHP program to find the diagonal
// of the octagon
 
// Function to find the diagonal
// of the octagon
function octadiagonal($a)
{
 
    // side cannot be negative
    if ($a < 0)
        return -1;
 
    // diagonal of the octagon
    return $a * sqrt(4 + (2 * sqrt(2)));
}
 
// Driver code
 
    $a = 4;
    echo octadiagonal($a) ;
 
// This code is contributed 
// by inder_verma
 
?>

Javascript

<script>
// javascript  Program to find the diagonal 
// of the octagon 
 
// Function to find the diagonal 
// of the octagon 
function octadiagonal(a) 
{ 
   
    // side cannot be negative 
    if (a < 0) 
        return -1; 
   
    // diagonal of the octagon 
    return a * Math.sqrt(4 + (2 * Math.sqrt(2))); 
} 
 
var a = 4; 
document.write( octadiagonal(a).toFixed(5)); 
 
// This code is contributed by 29AjayKumar 
</script>

Output:

10.4525

Time complexity: O(1), since there is no loop or recursion.

Auxiliary Space: O(1), since no extra space has been taken.

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