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 = 10 
Output: 57
Input: a = 19 
Output: 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 * r²) / 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

Time Complexity: O(1)

Auxiliary Space: O(1)