# 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

```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++

 `// C++ Program to find the area of the square ` `// inscribed within the circle which in turn ` `// is inscribed in an equilateral triangle ` `#include ` `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

 `// 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.. ` `    ``} ` `} `

## 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 `

## 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 `

## PHP

 ` `

Output:

```0.527046
```

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Improved By : inderDuMCA, AnkitRai01