Area of hexagon with given diagonal length

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++

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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.    
}

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PHP


Output:

Area of Hexagon:  64.952 

Time Complexity: O(1)



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Improved By : AnkitRai01, rituraj_jain, jit_t