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 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
// 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
# 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#
// 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// 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 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> |
Output:
57
Time Complexity: O(1)
Auxiliary Space: O(1)
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