Given here is an equilateral triangle with side length a, which inscribes a circle, which in turn inscribes a square. The task is to find the area of this square.
Examples:
Input: a = 6 Output: 1 Input: a = 10 Output: 0.527046
Approach:
let r be the radius of circle,
hence it is the inradius of equilateral triangle, so r = a /(2 * ?3)
diagonal of square, d = diameter of circle = 2 * r = a/ ?3
So, area of square, A = 0.5 * d * d
hence A = (1/2) * (a^2) / (3) = (a^2/6)
Below is the implementation of the above approach:
// C++ Program to find the area of the square // inscribed within the circle which in turn // is inscribed in an equilateral triangle #include <bits/stdc++.h> using namespace std;
// Function to find the area of the square float area( float a)
{ // a cannot be negative
if (a < 0)
return -1;
// area of the square
float area = sqrt (a) / 6;
return area;
} // Driver code int main()
{ float a = 10;
cout << area(a) << endl;
return 0;
} |
// Java Program to find the area of the square // inscribed within the circle which in turn // is inscribed in an equilateral triangle import java.io.*;
class GFG {
// Function to find the area of the square static float area( float a)
{ // a cannot be negative
if (a < 0 )
return - 1 ;
// area of the square
float area = ( float )Math.sqrt(a) / 6 ;
return area;
} // Driver code public static void main (String[] args) {
float a = 10 ;
System.out.println( area(a));
// This code is contributed // by inder_verma.. }
} |
# Python3 Program to find the area # of the square inscribed within # the circle which in turn is # inscribed in an equilateral triangle # import everything from math lib. from math import *
# Function to find the area # of the square def area(a):
# a cannot be negative
if a < 0 :
return - 1
# area of the square
area = sqrt(a) / 6
return area
# Driver code if __name__ = = "__main__" :
a = 10
print ( round (area(a), 6 ))
# This code is contributed by ANKITRAI1 |
// C# Program to find the area // of the square inscribed within // the circle which in turn is // inscribed in an equilateral triangle using System;
class GFG
{ // Function to find the area // of the square static float area( float a)
{ // a cannot be negative
if (a < 0)
return -1;
// area of the square
float area = ( float )Math.Sqrt(a) / 6;
return area;
} // Driver code public static void Main ()
{ float a = 10;
Console.WriteLine(area(a));
} } // This code is contributed // by inder_verma |
<?php // PHP Program to find the area // of the square inscribed within // the circle which in turn is // inscribed in an equilateral triangle // Function to find the // area of the square function area( $a )
{ // a cannot be negative
if ( $a < 0)
return -1;
// area of the square
$area = sqrt( $a ) / 6;
return $area ;
} // Driver code $a = 10;
echo area( $a );
// This code is contributed // by inder_verma ?> |
<script> // javascript Program to find the area of the square // inscribed within the circle which in turn // is inscribed in an equilateral triangle // Function to find the area of the square function area(a)
{ // a cannot be negative
if (a < 0)
return -1;
// area of the square
var area = Math.sqrt(a) / 6;
return area;
} // Driver code var a = 10;
document.write( area(a).toFixed(6)); // This code contributed by shikhasingrajput </script> |
0.527046
Time complexity : O(log(a)) for given side a, as complexity of inbuilt sqrt function
Auxiliary Space : O(1)