# 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 = 10

Output:21.65

Explanation:

Maximum area of rectangle inscribed in an equilateral triangle of side 10 is 21.65.

Input:A = 12

Output:31.176

Explanation:

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 ` |

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## 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 ` |

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## 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)) ` |

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## 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 ` |

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**Output:**

42.434

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