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Find area of the Circle when the area of inscribed Square is given

  • Difficulty Level : Hard
  • Last Updated : 24 Nov, 2021

Given area of square inscribed in a circle as N, the task is to calculate the area of circle in which the square is inscribed.

Examples: 

Input: N = 4 
Output: 6.283

Input: N = 10
Output:  15.707

 

Approach:

Consider the below image:
 

 

  • Let the area of the square is ‘A’
  • The side of the square is given by = A**(1/2)
  • A right-angled triangle is formed by the two sides of the square and the diameter of the circle
  • The hypotenuse of triangle will be diameter of circle
  • The diameter of circle ‘D’ is calculated as ((A * A) + (A * A))**(1/2)
  • The radius of circle ‘r’ is given by D/2
  • The resultant area of the circle is pi*r*r

Below is the implementation of the above approach: 

C++




#include <iostream>
#include<math.h>
#include <iomanip>
using namespace std;
 
// Function to calculate the area of circle
double areaOfCircle(double a)
{
    // declaring pi
    double pi=2*acos(0.0);
       
    // Side of the square
    double side = pow(a,(1.0 / 2));
 
    // Diameter of circle
    double D =pow( ((side * side) + (side * side)) ,(1.0 / 2));
 
    // Radius of circle
    double R = D / 2;
 
    // Area of circle
    double Area = pi * (R * R);
 
    return Area;
 
}
 //Driver Code
int main() {
    
    double areaOfSquare = 4;
    cout<<setprecision(15)<<areaOfCircle(areaOfSquare);
    return 0;
}
// This code is contributed by ANKITKUMAR34

Java




// Java code for the above approach
import java.util.*;
 
class GFG
{
   
    // Function to calculate the area of circle
    static double areaOfCircle(double a)
    {
 
        // Side of the square
        double side = Math.pow(a, (1.0 / 2));
 
        // Diameter of circle
        double D = Math.pow(((side * side) + (side * side)),
                            (1.0 / 2));
 
        // Radius of circle
        double R = D / 2;
 
        // Area of circle
        double Area = Math.PI * (R * R);
 
        return Area;
    }
   
    // Driver Code
    public static void main(String[] args)
    {
        double areaOfSquare = 4;
        System.out.println(areaOfCircle(areaOfSquare));
    }
}
 
// This code is contribute by Potta Lokesh

Python3




# Python program for the above approach
import math
 
# Function to calculate the area of circle
def areaOfCircle(a):
 
    # Side of the square
    side = a**(1 / 2)
 
    # Diameter of circle
    D = ((side * side) + (side * side))**(1 / 2)
 
    # Radius of circle
    R = D / 2
 
    # Area of circle
    Area = math.pi * (R * R)
 
    return Area
 
# Driver Code
areaOfSquare = 4
print(areaOfCircle(areaOfSquare))

C#




// C# code for the above approach
using System;
 
class GFG
{
   
    // Function to calculate the area of circle
    static double areaOfCircle(double a)
    {
 
        // Side of the square
        double side = Math.Pow(a, (1.0 / 2));
 
        // Diameter of circle
        double D = Math.Pow(((side * side) + (side * side)),
                            (1.0 / 2));
 
        // Radius of circle
        double R = D / 2;
 
        // Area of circle
        double Area = Math.PI * (R * R);
 
        return Area;
    }
   
    // Driver Code
    public static void Main()
    {
        double areaOfSquare = 4;
        Console.Write(areaOfCircle(areaOfSquare));
    }
}
 
// This code is contribute by Samim Hossain Mondal.

Javascript




<script>
 
// Function to calculate the area of circle
function areaOfCircle(a) {
  // declaring pi
  let pi = 2 * Math.acos(0.0);
 
  // Side of the square
  let side = Math.pow(a, (1.0 / 2));
 
  // Diameter of circle
  let D = Math.pow(((side * side) + (side * side)), (1.0 / 2));
 
  // Radius of circle
  let R = D / 2;
 
  // Area of circle
  let Area = Math.PI * (R * R);
 
  return Area;
 
}
//Driver Code
 
let areaOfSquare = 4;
document.write(areaOfCircle(areaOfSquare));
 
// This code is contributed by gfgking
</script>
Output
6.283185307179588

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


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