# Maximum area of rectangle inscribed in an equilateral triangle

Given an integer **A**, which denotes the side of an equilateral triangle, the task is to find the maximum area of the rectangle that can be inscribed in the triangle.**Examples:**

Input:A = 10Output:21.65Explanation:

Maximum area of rectangle inscribed in an equilateral triangle of side 10 is 21.65.Input:A = 12Output:31.176Explanation:

Maximum area of rectangle inscribed in an equilateral triangle of side 12 is 31.176.

**Approach:** The idea is to use the fact that interior angles of an equilateral triangle is 60^{o}. Then, Draw the perpendicular from one of the side of the triangle and compute the sides of the rectangle with the help of below formulae

The length of Rectangle = (Side of Equilateral Triangle)/2

The breadth of Rectangle = sqrt(3) * (Side of Equilateral Triangle)/4

Then, Maximum area of the rectangle will be

Below is the implementation of the above approach:

## C++

`// CPP implementation to find the` `// maximum area inscribed in an` `// equilateral triangle` `#include<bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the maximum area` `// of the rectangle inscribed in an` `// equilateral triangle of side S` `double` `solve(` `int` `s)` `{` ` ` `// Maximum area of the rectangle` ` ` `// inscribed in an equilateral` ` ` `// triangle of side S` ` ` `double` `area = (1.732 * ` `pow` `(s, 2))/8;` ` ` `return` `area;` ` ` `}` ` ` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 14;` ` ` `cout << solve(n);` `}` ` ` `// This code is contributed by Surendra_Gangwar` |

## Java

`// Java implementation to find the` `// maximum area inscribed in an` `// equilateral triangle` `class` `GFG` `{` ` ` `// Function to find the maximum area` ` ` `// of the rectangle inscribed in an` ` ` `// equilateral triangle of side S` ` ` `static` `double` `solve(` `int` `s)` ` ` `{` ` ` `// Maximum area of the rectangle` ` ` `// inscribed in an equilateral` ` ` `// triangle of side S` ` ` `double` `area = (` `1.732` `* Math.pow(s, ` `2` `))/` `8` `;` ` ` `return` `area;` ` ` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `n = ` `14` `;` ` ` `System.out.println(solve(n));` ` ` `}` `}` ` ` `// This article is contributed by Apurva raj` |

## Python3

`# Python3 implementation to find the` `# maximum area inscribed in an` `# equilateral triangle` `# Function to find the maximum area` `# of the rectangle inscribed in an` `# equilateral triangle of side S` `def` `solve(s):` ` ` ` ` `# Maximum area of the rectangle` ` ` `# inscribed in an equilateral` ` ` `# triangle of side S` ` ` `area ` `=` `(` `1.732` `*` `s` `*` `*` `2` `)` `/` `8` ` ` `return` `area` ` ` ` ` `# Driver Code` `if` `__name__` `=` `=` `'__main__'` `:` ` ` `n ` `=` `14` ` ` `print` `(solve(n))` |

## C#

`// C# implementation to find the` `// maximum area inscribed in an` `// equilateral triangle` `using` `System;` `class` `GFG` `{` ` ` `// Function to find the maximum area` ` ` `// of the rectangle inscribed in an` ` ` `// equilateral triangle of side S` ` ` `static` `double` `solve(` `int` `s)` ` ` `{` ` ` `// Maximum area of the rectangle` ` ` `// inscribed in an equilateral` ` ` `// triangle of side S` ` ` `double` `area = (1.732 * Math.Pow(s, 2))/8;` ` ` `return` `area;` ` ` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `Main(String[] args)` ` ` `{` ` ` `int` `n = 14;` ` ` `Console.WriteLine(solve(n));` ` ` `}` `}` `// This code is contributed by Rajput-Ji` |

## Javascript

`<script>` `// Javascript implementation to find the` `// maximum area inscribed in an` `// equilateral triangle` `// Function to find the maximum area` `// of the rectangle inscribed in an` `// equilateral triangle of side S` `function` `solve(s)` `{` ` ` `// Maximum area of the rectangle` ` ` `// inscribed in an equilateral` ` ` `// triangle of side S` ` ` `let area = (1.732 * Math.pow(s, 2))/8;` ` ` `return` `area;` ` ` `}` ` ` `// Driver Code` ` ` `let n = 14;` ` ` `document.write(solve(n));` `// This code is contributed by Manoj` `</script>` |

**Output:**

42.434

**Time complexity**: O(1) as constant operations are done

**Auxiliary Space: **O(1)