# 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

**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 biggest square ` `// which can be inscribed within the semicircle ` `#include <bits/stdc++.h> ` `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; ` `} ` |

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## Java

`// Java Program to find 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. ` |

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## Python3

`# Python 3 program to find 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 ` |

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## C#

`// C# Program to find 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 ` |

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## PHP

`<?php ` `// PHP Program to find the ` `// biggest square which can be ` `// inscribed within the semicircle ` ` ` `// Function to find the area ` `// of the squaare ` `function` `squarearea(` `$r` `) ` `{ ` ` ` ` ` `// the radius cannot be negative ` ` ` `if` `(` `$r` `< 0) ` ` ` `return` `-1; ` ` ` ` ` `// area of the square ` ` ` `$a` `= 4 * (pow(` `$r` `, 2) / 5); ` ` ` ` ` `return` `$a` `; ` `} ` ` ` `// Driver code ` `$r` `= 5; ` `echo` `squarearea(` `$r` `); ` ` ` `// This code is contributed ` `// by Shivi_Aggarwal ` `?> ` |

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**Output:**

20

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