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

19 Apr, 2021
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: 57Input: 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++
Java
Python3
C#
PHP
Javascript
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std; // Function to return the area// of the shaded regionfloat 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 codeint main(){    float a = 10;    cout << findAreaShaded(a);     return 0;}
// Java implementation of the approachclass 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 implementation of the approach # Function to return the area# of the shaded regiondef 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 codeif __name__ == '__main__':    a = 10    print(findAreaShaded(a))
// C# implementation of the approachusing 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 implementation of the approach // Function to return the area// of the shaded regionfunction 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?>
<script> // Javascript implementation of the approach // Function to return the area// of the shaded regionfunction 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>
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