Area of a circle inscribed in a regular hexagon

Given a regular Hexagon with side length a, the task is to find the area of the circle inscribed in it, given that, the circle is tangent to each of the six sides.

Examples:

Input: a = 4
Output: 37.68

Input: a = 10
Output: 235.5



Approach:
From the figure, it is clear that, we can divide the regular hexagon into 6 identical equilateral triangles.
We take one triangle OAB, with O as the centre of the hexagon or circle, & AB as one side of the hexagon.
Let M be mid-point of AB, OM would be the perpendicular bisector of AB, angle AOM = 30 deg

Then in right angled triangle OAM,

tanx = tan30 = 1/√3
So, a/2r = 1/√3
Therefore, r = a√3/2
Area of circle, A =Πr²=Π3a^2/4

Below is the implementation of the approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ Program to find the area of the circle
// which can be inscribed within the hexagon
#include <bits/stdc++.h>
using namespace std;
  
// Function to find the area
// of the inscribed circle
float circlearea(float a)
{
  
    // the side cannot be negative
    if (a < 0)
        return -1;
  
    // area of the circle
    float A = (3.14 * 3 * pow(a, 2)) / 4;
  
    return A;
}
  
// Driver code
int main()
{
    float a = 4;
    cout << circlearea(a) << endl;
  
    return 0;
}

chevron_right






                        filter_none









Java














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















//Java program to to find the  


//area of the circle  


//which can be inscribed within the hexagon 


  


import java.util.*; 


  


class solution 


{ 


static double circlearea(double a) 


{ 


  


// the side cannot be negative 


    if (a < 0) 


    return -1; 


  


// area of the circle 


    double A = (3.14 * 3 * Math.pow(a,2) ) / 4; 


  


    return A; 


} 


public static void main(String arr[]) 


{ 


    double a = 4; 


    System.out.println(circlearea(a)); 


} 


} 



















                        chevron_right







                        filter_none









Python 3














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















# Python 3 program to find the  


# area of the circle  


# which can be inscribed within the hexagon 


  


# Function to find the area  


# of the inscribed circle  


def circlearea(a) : 


  


    # the side cannot be negative  


    if a < 0 : 


        return -1


  


    #  area of the circle 


    A = (3.14 * 3 * pow(a,2)) / 4


  


    return A 


  


  


# Driver code      


if __name__ == "__main__" : 


  


    a = 4


    print(circlearea(a)) 


  


  


# This code is contributed by ANKITRAI1 



















                        chevron_right







                        filter_none









C#














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// C# program to to find   


// the area of the circle  


// which can be inscribed  


// within the hexagon 


using System; 


  


class GFG 


{ 


static double circlearea(double a) 


{ 


  


    // the side cannot be negative 


    if (a < 0) 


    return -1; 


  


    // area of the circle 


    double A = (3.14 * 3 *  


                Math.Pow(a, 2)) / 4; 


  


    return A; 


} 


  


// Driver Code 


public static void Main() 


{ 


    double a = 4; 


    Console.WriteLine(circlearea(a)); 


} 


} 


  


// This code is contributed 


// by inder_verma 



















                        chevron_right







                        filter_none









PHP














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















<?php 


// PHP Program to find the area of  


// the circle which can be inscribed  


// within the hexagon 


  


// Function to find the area 


// of the inscribed circle 


function circlearea($a) 


{ 


  


    // the side cannot be negative 


    if ($a < 0) 


        return -1; 


  


    // area of the circle 


    $A = (3.14 * 3 * pow($a, 2)) / 4; 


  


    return $A; 


} 


  


// Driver code 


$a = 4; 


echo circlearea($a) . "\n"; 


  


// This code is contributed  


// by Akanksha Rai(Abby_akku) 



















                        chevron_right







                        filter_none











Output:


37.68






          
          
          
          

            

    

        My Personal Notes
        arrow_drop_up
    

    

        
        

            
            
        

    


Recommended Posts:
IshwarGupta
Budding Web DeveloperKeen learnerAverage CoderDancer&Social Activist
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on  the "Improve Article" button below.