# Area of a Circumscribed Circle of a Square

• Difficulty Level : Basic
• Last Updated : 09 Jun, 2022

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

## C++

 `// C++ Program to find the``// area of a circumscribed circle``#include ``#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

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## Javascript

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Output

` Area of an circumscribed circle is : 56.55 `

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

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