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

• Last Updated : 27 Aug, 2022

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 * âˆš3)
diagonal of square, d = diameter of circle = 2 * r = a/ âˆš3
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

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## Javascript

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Output:

`0.527046`

Time complexity : O(log(a)) for given side a, as complexity of inbuilt sqrt function
Auxiliary Space : O(1)

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