Length of the Diagonal of the Octagon

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.