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

• Last Updated : 16 Mar, 2021

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 ``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

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## Javascript

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Output:
`37.5`

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