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Area of hexagon with given diagonal length
  • Last Updated : 10 Mar, 2021

You are given the length of the diagonal of a hexagon, d. Your task is to find the area of that hexagon. 
Examples: 
 

Input :   5
Output :   Area of Hexagon: 16.238

Input : 10
Output : Area of Hexagon: 64.9519

Hexagon 
Hexagon is a regular polygon having six equal sides and all equal angles. The interior angles of Hexagon are of 120 degrees each and the sum of all angles of a Hexagon is 720 degrees.
 

Hexagon

Let d be the diagonal of Hexagon, then the formula to find the area of Hexagon given by 
Area =

     $$ \frac{3 \sqrt{3}d^2}{8} $$



How does above formula work? 
We know that area of hexagon with side length a = (3 √3(a)2 ) / 2. Since all sides are of same size and angle is 120 degree, d = 2a or a = d/2. After putting this value, we get area as (3 √3(d)2 ) / 8. 
Below is the implementation . 
 

C++




// C++ program to find the area of Hexagon with given diagonal
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate area
float hexagonArea(float d)
{
    // Formula to find area
    return (3 * sqrt(3) * pow(d, 2)) / 8;
}
 
// Main
int main()
{
    float d = 10;
    cout << "Area of hexagon: " << hexagonArea(d);
    return 0;
}

Java




// Java program to find the area of
// Hexagon with given diagonal
import java.lang.Math;
 
public class GfG {
 
    // Function to calculate area
    public static float hexagonArea(float d)
    {
        // Formula to find area
        return (float)((3 * Math.sqrt(3) * d * d) / 8);
    }
 
    public static void main(String []args) {
        float d = 10;
        System.out.println("Area of hexagon: " + hexagonArea(d));
    }
}
 
// This code is contributed by Rituraj Jain

Python3




# Python3 program to find the area
# of Hexagon with given diagonal
from math import sqrt
 
# Function to calculate area
def hexagonArea(d) :
 
    # Formula to find area
    return (3 * sqrt(3) * pow(d, 2)) / 8
 
# Driver ode
if __name__ == "__main__" :
 
    d = 10
    print("Area of hexagon:",
           round(hexagonArea(d), 3))
 
# This code is contributed by Ryuga

C#




// C# program to find the area of
// Hexagon with given diagonal
 
using System;
 
public class GFG{
     
    // Function to calculate area
    public static float hexagonArea(float d)
    {
        // Formula to find area
        return (float)((3 * Math.Sqrt(3) * d * d) / 8);
    }
 
 
//Code driven
    static public void Main (){
            float d = 10;
        Console.WriteLine("Area of hexagon: " + hexagonArea(d));
    }
//This code is contributed by Tushil.   
}

PHP




<?php
// PHP program to find the area of
// Hexagon with given diagonal
 
// Function to calculate area
function hexagonArea($d)
{
    // Formula to find area
    return (3 * sqrt(3) * pow($d, 2)) / 8;
}
 
// Driver Code
$d = 10;
echo "Area of hexagon: ",
         hexagonArea($d);
 
// This code is contributed by ajit.
?>

Javascript




<script>
// JavaScript program to find
// the area of Hexagon with given diagonal
 
// Function to calculate area
function hexagonArea( d)
{
    // Formula to find area
    return (3 * Math.sqrt(3) * Math.pow(d, 2)) / 8;
}
 
// Driver Code
 
    let d = 10;
    document.write("Area of hexagon: " + hexagonArea(d).toFixed(3));
     
// This code is contributed by todaysgaurav
 
</script>

Output: 

Area of Hexagon:  64.952 

Time Complexity: O(1)
 

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