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

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 <bits/stdc++.h> ` `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; ` `} ` |

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## 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 ` |

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## 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 ` |

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## 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.. ` |

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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 a hexagon ` ` ` `// Function to find the area ` `// of the square ` `function` `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` `$area` `; ` `} ` ` ` `// Driver code ` `$a` `= 5; ` `echo` `area(` `$a` `) . ` `"\n"` `; ` ` ` `// This code is contributed ` `// by Akanksha Rai(Abby_akku) ` `?> ` |

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**Output:**

37.5

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