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;` `}` |

## 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

`<?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` `?>` |

## Javascript

`<script>` `// javascript 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` ` ` `var` `area = Math.sqrt(a) / 6;` ` ` `return` `area;` `}` `// Driver code` `var` `a = 10;` `document.write( area(a).toFixed(6));` `// This code contributed by shikhasingrajput` `</script>` |

**Output:**

0.527046

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready.