# Area of a square inscribed in a circle which is inscribed in an equilateral triangle

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

rbe the radius of circle,

hence it is the inradius of equilateral triangle, sor = a /(2 * √3)

diagonal of square,d= diameter of circle =2 * r = a/ √3

So, area of square,A = 0.5 * d * d

henceA = (1/2) * (a^2) / (3) = (a^2/6)

Below is the implementation of the above approach:

## C++

`// 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; ` `} ` |

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## Java

`// 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.. ` ` ` `} ` `} ` |

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## Python 3

`# 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 ` |

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## C#

`// 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 ` |

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## PHP

`<?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 ` `?> ` |

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**Output:**

0.527046

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