Largest square that can be inscribed in a semicircle

Given a semicircle with radius r, we have to find the largest square that can be inscribed in the semicircle, with base lying on the diameter.

Examples:

```Input: r = 5
Output: 20

Input: r = 8
Output: 51.2
```

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Let r be the radius of the semicircle & a be the side length of the square.
From the figure we can see that, centre of the circle is also the midpoint of the base of the square.So in the right angled triangle AOB, from Pythagorus Theorem:

a^2 + (a/2)^2 = r^2

5*(a^2/4) = r^2

a^2 = 4*(r^2/5) i.e. area of the square

Below is the implementation of the above approach:

C++

 `// C++ Program to find the the biggest square ` `// which can be inscribed within the semicircle ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the area ` `// of the squaare ` `float` `squarearea(``float` `r) ` `{ ` ` `  `    ``// the radius cannot be negative ` `    ``if` `(r < 0) ` `        ``return` `-1; ` ` `  `    ``// area of the square ` `    ``float` `a = 4 * (``pow``(r, 2) / 5); ` ` `  `    ``return` `a; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``float` `r = 5; ` `    ``cout << squarearea(r) << endl; ` ` `  `    ``return` `0; ` `} `

Java

 `// Java Program to find the the biggest square ` `// which can be inscribed within the semicircle ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` ` `  ` `  `// Function to find the area ` `// of the squaare ` `static` `float` `squarearea(``float` `r) ` `{ ` ` `  `    ``// the radius cannot be negative ` `    ``if` `(r < ``0``) ` `        ``return` `-``1``; ` ` `  `    ``// area of the square ` `    ``float` `a = ``4` `* (``float``)(Math.pow(r, ``2``) / ``5``); ` ` `  `    ``return` `a; ` `} ` ` `  `// Driver code ` ` `  `    ``public` `static` `void` `main (String[] args) { ` `         ``float` `r = ``5``; ` `    ``System.out.println( squarearea(r)); ` `    ``} ` `} ` `// This code is contributed by chandan_jnu. `

Python3

 `# Python 3 program to find the the  ` `# biggest square which can be  ` `# inscribed within the semicircle ` ` `  `# Function to find the area ` `# of the squaare ` `def` `squarearea(r): ` ` `  `    ``# the radius cannot be ` `    ``# negative ` `    ``if` `(r < ``0``): ` `        ``return` `-``1` ` `  `    ``# area of the square ` `    ``a ``=` `4` `*` `(``pow``(r, ``2``) ``/` `5``) ` ` `  `    ``return` `a ` ` `  `# Driver code ` `if` `__name__ ``=``=` `"__main__"``: ` `     `  `    ``r ``=` `5` `    ``print``(``int``(squarearea(r))) ` ` `  `# This code is contributed ` `# by ChitraNayal `

C#

 `// C# Program to find the the  ` `// biggest square which can be ` `// inscribed within the semicircle ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to find the  ` `// area of the squaare ` `static` `float` `squarearea(``float` `r) ` `{ ` ` `  `    ``// the radius cannot be negative ` `    ``if` `(r < 0) ` `        ``return` `-1; ` ` `  `    ``// area of the square ` `    ``float` `a = 4 * (``float``)(Math.Pow(r, 2) / 5); ` ` `  `    ``return` `a; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main () ` `{ ` `    ``float` `r = 5; ` `    ``Console.WriteLine(squarearea(r)); ` `} ` `} ` ` `  `// This code is contributed  ` `// by anuj_67 `

PHP

 ` `

Output:

```20
```

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