# Find the area of the shaded region formed by the intersection of four semicircles in a square

Given the length of the side of a square **a**, the task is to find the area of the shaded region formed by the intersection of four semicircles in a square as shown in the image below:

**Examples:**

Input:a = 10Output:57Input:a = 19Output:205.77

**Approach:** Area of the shaded region will be:

Area(semicircle1) + Area(semicircle2) + Area(semicircle3) + Area(semicircle4) – Area(square).

Since all semicircles are of same radius, therefore, area of all semicircles will be equal. So, the above formula can be written as:4*(Area of Semicircle) – Area(Square)

The area of a semicircle is **(3.14 * r ^{2}) / 2** where

**r**is the radius of the semicircle which is equal to

**a / 2**.

Hence,

**Area of the shaded region = 4 * (3.14 * (a * a) / 8 ) – a * a**

Below is the implementation of the above approach:

## C++

`// C++ implementation of the approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to return the area` `// of the shaded region` `float` `findAreaShaded(` `float` `a)` `{` ` ` `// Area of the square` ` ` `float` `sqArea = a * a;` ` ` `// Area of the semicircle` ` ` `float` `semiCircleArea = (3.14 * (a * a) / 8);` ` ` `// There are 4 semicircles` ` ` `// shadedArea = Area of 4 semicircles - Area of square` ` ` `float` `ShadedArea = 4 * semiCircleArea - sqArea;` ` ` `return` `ShadedArea;` `}` `// Driver code` `int` `main()` `{` ` ` `float` `a = 10;` ` ` `cout << findAreaShaded(a);` ` ` `return` `0;` `}` |

## Java

`// Java implementation of the approach` `class` `GFG {` ` ` `// Function to return the area` ` ` `// of the shaded region` ` ` `static` `float` `findAreaShaded(` `float` `a)` ` ` `{` ` ` `// Area of the square` ` ` `float` `sqArea = a * a;` ` ` `// Area of the semicircle` ` ` `float` `semiCircleArea = (` `float` `)(` `3.14` `* (a * a) / ` `8` `);` ` ` `// There are 4 semicircles` ` ` `// shadedArea = Area of 4 semicircles - Area of square` ` ` `float` `ShadedArea = ` `4` `* semiCircleArea - sqArea;` ` ` `return` `ShadedArea;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `float` `a = ` `10` `;` ` ` `System.out.println(findAreaShaded(a));` ` ` `}` `}` |

## Python3

`# Python3 implementation of the approach` `# Function to return the area` `# of the shaded region` `def` `findAreaShaded(a):` ` ` ` ` `# Area of the square` ` ` `sqArea ` `=` `a ` `*` `a;` ` ` `# Area of the semicircle` ` ` `semiCircleArea ` `=` `(` `3.14` `*` `(a ` `*` `a ) ` `/` `8` `)` ` ` `# There are 4 semicircles` ` ` `# shadedArea = Area of 4 semicircles - Area of square` ` ` `ShadedArea ` `=` `4` `*` `semiCircleArea ` `-` `sqArea ;` ` ` `return` `ShadedArea;` `# Driver code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `a ` `=` `10` ` ` `print` `(findAreaShaded(a))` |

## C#

`// C# implementation of the approach` `using` `System;` `class` `GFG` `{` ` ` `// Function to return the area` ` ` `// of the shaded region` ` ` `static` `float` `findAreaShaded(` `float` `a)` ` ` `{` ` ` `// Area of the square` ` ` `float` `sqArea = a * a;` ` ` `// Area of the semicircle` ` ` `float` `semiCircleArea = (` `float` `)(3.14 * (a * a) / 8);` ` ` `// There are 4 semicircles` ` ` `// shadedArea = Area of 4 semicircles - Area of square` ` ` `float` `ShadedArea = 4 * semiCircleArea - sqArea;` ` ` `return` `ShadedArea;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `float` `a = 10;` ` ` `Console.WriteLine(findAreaShaded(a));` ` ` `}` `}` `// This code is contributed by mohit kumar 29` |

## PHP

`<?php` `// PHP implementation of the approach` `// Function to return the area` `// of the shaded region` `function` `findAreaShaded(` `$a` `)` `{` ` ` `// Area of the square` ` ` `$sqArea` `= ` `$a` `* ` `$a` `;` ` ` `// Area of the semicircle` ` ` `$semiCircleArea` `= (3.14 * (` `$a` `* ` `$a` `) / 8);` ` ` `// There are 4 semicircles` ` ` `// shadedArea = Area of 4 semicircles -` ` ` `// Area of square` ` ` `$ShadedArea` `= 4 * ` `$semiCircleArea` `- ` `$sqArea` `;` ` ` `return` `$ShadedArea` `;` `}` `// Driver code` `$a` `= 10;` `echo` `findAreaShaded(` `$a` `);` `// This code is contributed by Ryuga` `?>` |

## Javascript

`<script>` `// Javascript implementation of the approach` `// Function to return the area` `// of the shaded region` `function` `findAreaShaded( a)` `{` ` ` `// Area of the square` ` ` `let sqArea = a * a;` ` ` `// Area of the semicircle` ` ` `let semiCircleArea = (3.14 * (a * a) / 8);` ` ` `// There are 4 semicircles` ` ` `// shadedArea = Area of 4 semicircles - Area of square` ` ` `let ShadedArea = 4 * semiCircleArea - sqArea;` ` ` `return` `ShadedArea;` `}` ` ` `// driver code` ` ` `let a = 10;` ` ` `document.write(findAreaShaded(a));` ` ` `</script>` |

**Output:**

57

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