Given a regular hexagon with side A, which inscribes a circle of radius r, which in turn inscribes a square of side a.The task is to find the area of this square.
Examples:
Input : A = 5 Output : 37.5 Input : A = 8 Output : 96
Approach:
We know the radius of the circle inscribed within the hexagon is, r=A?3/2(Please refer here)
Also, side length of circle within the circle is, a=?r=?3A/?2
So, Area of the Square, Area=(?3A/?2)^2
C++
// C++ Program to find the area of the square // inscribed within the circle which in turn // is inscribed in a hexagon #include <bits/stdc++.h> using namespace std;
// Function to find the area of the square float area( float a)
{ // side of hexagon cannot be negative
if (a < 0)
return -1;
// area of the square
float area = pow ((a * sqrt (3)) / ( sqrt (2)), 2);
return area;
} // Driver code int main()
{ float a = 5;
cout << area(a) << endl;
return 0;
} |
Java
// Java Program to find the area of the square // inscribed within the circle which in turn // is inscribed in a hexagon import java.io.*;
class GFG {
// Function to find the area of the square static float area( float a)
{ // side of hexagon cannot be negative
if (a < 0 )
return - 1 ;
// area of the square
float area = ( float )Math.pow((a * Math.sqrt( 3 )) / (Math.sqrt( 2 )), 2 );
return area;
} // Driver code public static void main (String[] args) {
float a = 5 ;
System.out.println( area(a));
}
} // This code is contributed by ajit |
Python3
# Python 3 Program to find the area # of the square inscribed within the # circle which in turn is inscribed # in a hexagon from math import pow , sqrt
# Function to find the area # of the square def area(a):
# side of hexagon cannot
# be negative
if (a < 0 ):
return - 1
# area of the square
area = pow ((a * sqrt( 3 )) /
(sqrt( 2 )), 2 )
return area
# Driver code if __name__ = = '__main__' :
a = 5
print ( "{0:.3}" . format (area(a)))
# This code is contributed # by SURENDRA_GANGWAR |
C#
// C# Program to find the area of // the square inscribed within the // circle which in turn is inscribed // in a hexagon using System;
class GFG
{ // Function to find the area // of the square static float area( float a)
{ // side of hexagon cannot be negative
if (a < 0)
return -1;
// area of the square
float area = ( float )Math.Pow((a * Math.Sqrt(3)) /
(Math.Sqrt(2)), 2);
return area;
} // Driver code public static void Main ()
{ float a = 5;
Console.WriteLine( area(a));
} } // This code is contributed by inder_verma.. |
PHP
<?php // PHP Program to find the area // of the square inscribed within // the circle which in turn is // inscribed in a hexagon // Function to find the area // of the square function area( $a )
{ // side of hexagon cannot
// be negative
if ( $a < 0)
return -1;
// area of the square
$area = pow(( $a * sqrt(3)) /
(sqrt(2)), 2);
return $area ;
} // Driver code $a = 5;
echo area( $a ) . "\n" ;
// This code is contributed // by Akanksha Rai(Abby_akku) ?> |
Javascript
<script> // javascript Program to find the area of the square // inscribed within the circle which in turn // is inscribed in a hexagon // Function to find the area of the square function area(a)
{ // side of hexagon cannot be negative
if (a < 0)
return -1;
// area of the square
var area = Math.pow((a * Math.sqrt(3)) / (Math.sqrt(2)), 2);
return area;
} // Driver code var a = 5;
document.write( area(a).toFixed(5)); // This code contributed by shikhasingrajput </script> |
Output:
37.5
Time complexity: O(1)
Auxiliary Space: O(1)