# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

/blockquote>

## 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

 ` `

Output :

``` Area of an circumscribed circle is : 56.55
```

## tags:

Geometric School Programming circle Geometric