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

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 = 4Output:6.283

Input:N = 10Output: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)

*O(1)*

**Auxiliary Space:**