# Area of a Circumscribed Circle of a Square

Given the side of a square then find the area of a Circumscribed circle around it.

Examples:

Input : a = 6 Output : Area of a circumscribed circle is : 56.55 Input : a = 4 Output : Area of a circumscribed circle is : 25.13

All four sides of a square are of equal length and all four angles are 90 degree. The circle is circumscribed on a given square shown by a shaded region in the below diagram.

**Properties of Circumscribed circle are as follows:**

- The center of the circumcircle is the point where the two diagonals of a square meet.
- Circumscribed circle of a square is made through the four vertices of a square.
- The radius of a circumcircle of a square is equal to the radius of a square.

Formula used to calculate the area of inscribed circle is:

(PI * a * a)/2

where, a is the side of a square in which a circle is circumscribed.How does this formula work?

We know area of circle = PI*r*r.

We also know radius of circle = (square diagonal)/2

Length of diagonal = ?(2*a*a)

Radius = ?(2*a*a)/2 = ?((a*a)/2)

Area = PI*r*r = (PI*a*a)/2

## C++

`// C++ Program to find the` `// area of a circumscribed circle` `#include <stdio.h>` `#define PI 3.14159265` `float` `areacircumscribed(` `float` `a)` `{` ` ` `return` `(a * a * (PI / 2));` `}` `// Driver code` `int` `main()` `{` ` ` `float` `a = 6;` ` ` `printf` `(` `" Area of an circumscribed circle is : %.2f "` `,` ` ` `areacircumscribed(a));` ` ` `return` `0;` `}` |

## Java

`// Java program to calculate` `// area of a circumscribed circle-square` `import` `java.io.*;` `class` `Gfg {` ` ` `// Utility Function` ` ` `static` `float` `areacircumscribed(` `float` `a)` ` ` `{` ` ` `float` `PI = ` `3` `.14159265f;` ` ` `return` `(a * a * (PI / ` `2` `));` ` ` `}` ` ` `// Driver Function` ` ` `public` `static` `void` `main(String arg[])` ` ` `{` ` ` `float` `a = ` `6` `;` ` ` `System.out.print(` `"Area of an circumscribed"` ` ` `+ ` `"circle is :"` `);` ` ` `System.out.println(areacircumscribed(a));` ` ` `}` `}` `// The code is contributed by Anant Agarwal.` |

## Python3

`# Python3 Program to find the` `# area of a circumscribed circle` `PI ` `=` `3.14159265` `def` `areacircumscribed(a):` ` ` `return` `(a ` `*` `a ` `*` `(PI ` `/` `2` `))` `# Driver code` `a ` `=` `6` `print` `(` `" Area of an circumscribed circle is :"` `,` ` ` `round` `(areacircumscribed(a), ` `2` `))` ` ` `# This code is contributed by Smitha Dinesh Semwal` |

## C#

`// C# Program to find the` `// area of a circumscribed circle` `using` `System;` `class` `GFG {` ` ` ` ` `public` `static` `double` `PI= 3.14159265 ;` ` ` `static` `float` `areacircumscribed(` `float` `a)` ` ` `{` ` ` `return` `(a * a * (` `float` `)(PI / 2));` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `float` `a = 6;` ` ` ` ` `Console.Write(` `" Area of an circumscribed"` ` ` `+ ` `" circle is : {0}"` `,` ` ` `Math.Round(areacircumscribed(a), 2));` ` ` `}` `}` `// This code is contributed by` `// Smitha Dinesh Semwal` |

## PHP

`<?php` `// PHP Program to find the` `// area of a circumscribed` `// circle` `$PI` `= 3.14159265;` `// function returns the area` `function` `areacircumscribed(` `$a` `)` `{` ` ` `global` `$PI` `;` ` ` `return` `(` `$a` `* ` `$a` `* (` `$PI` `/ 2));` `}` ` ` `// Driver code` ` ` `$a` `= 6;` ` ` `echo` `" Area of an circumscribed circle is : "` `,` ` ` `areacircumscribed(` `$a` `);` `// The code is contributed by anuj_67.` `?>` |

## Javascript

`<script>` `// Javascript Program to find the` `// area of a circumscribed circle` `function` `areacircumscribed(a)` `{` ` ` `return` `(a * a * (3.1415 / 2));` `}` `// Driver code` ` ` `let a = 6;` ` ` `document.write(` `" Area of an circumscribed circle is : "` `,` ` ` `areacircumscribed(a));` `// This code is contributed by Mayank Tyagi` `</script>` |

**Output**

Area of an circumscribed circle is : 56.55

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