Area of a square inscribed in a circle which is inscribed in a hexagon
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)