Area of the circle that has a square and a circle inscribed in it

Last Updated : 05 Dec, 2022

Given the side of a square that is kept inside a circle. It keeps expanding until all four of its vertices touch the circumference of the circle. Another smaller circle is kept inside the square now and it keeps expanding until its circumference touches all four sides of the square. The outer and the inner circle form a ring. Find the area of this shaded part as shown in the image below.

Examples:

Input: a = 3
Output: 7.06858

Input: a = 4
Output: 12.566371

Approach:

From the above figure, R = a / sqrt(2) can be derived where a is the side length of the square. The area of the outer circle is (pi * R * R).
Let s1 be the area of the outer circle (pi * R * R) and s2 be the area of the inner circle (pi * r * r). Then the area of the ring is s1 - s2.

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 required area float getArea(int a) {      // Calculate the area     float area = (M_PI * a * a) / 4.0;     return area; }  // Driver code int main() {     int a = 3;      cout << getArea(a);      return 0; }

Java

// Java implementation of the approach public class GFG {      // Function to return the required area     static float getArea(int a)     {          // Calculate the area         float area = (float)(Math.PI * a * a) / 4;         return area;     }      // Driver code     public static void main(String args[])     {         int a = 3;         System.out.println(getArea(a));     } }

Python3

# Python3 implementation of the approach import math   # Function to return the required area def getArea(a):          # Calculate the area     area = (math.pi * a * a) / 4     return area      # Driver code a = 3 print('{0:.6f}'.format(getArea(a)))

// C# implementation of the approach using System;  class GFG  {      // Function to return the required area     static float getArea(int a)     {          // Calculate the area         float area = (float)(Math.PI * a * a) / 4;         return area;     }      // Driver code     public static void Main()     {         int a = 3;         Console.Write(getArea(a));     } }  // This code is contributed by mohit kumar 29

JavaScript

<script>  // Javascript implementation of the approach  // Function to return the required area function getArea(a) {          // Calculate the area     var area = (Math.PI * a * a) / 4;     return area; }  // Driver Code  var a = 3;  document.write(getArea(a));  // This code is contributed by Kirti      </script>

Output

7.06858

Time Complexity: O(1)
Auxiliary Space: O(1)

Area of the circle that has a square and a circle inscribed in it

Bhargav_Thota

Improve

Article Tags :

Practice Tags :

Area of the circle that has a square and a circle inscribed in it

Similar Reads