# Program to calculate area of Circumcircle of an Equilateral Triangle

Given the length of sides of an equilateral triangle. We need to write a program to find the area of Circumcircle of the given equilateral triangle.
Examples:

```Input : side = 6
Output : Area of circumscribed circle is: 37.69

Input : side = 9
Output : Area of circumscribed circle is: 84.82 ```

All three sides of equilateral triangle are of equal length and all three interior angles are 60 degrees.
Properties of a Circumcircle are as follows:

• The center of the circumcircle is the point where the medians of the equilateral triangle intersect.
• Circumscribed circle of an equilateral triangle is made through the three vertices of an equilateral triangle.
• The radius of a circumcircle of an equilateral triangle is equal to (a / ?3), where ‘a’ is the length of the side of equilateral triangle.

Below image shows an equilateral triangle with circumcircle:

The formula used to calculate the area of circumscribed circle is:

`(?*a2)/3`

where a is the length of the side of the given equilateral triangle.

How this formulae works?

We know that area of circle = ?*r2, where r is the radius of given circle.
We also know that radius of Circumcircle of an equilateral triangle = (side of the equilateral triangle)/ ?3.
Therefore, area = ?*r2 = ?*a2/3.

## C++

 `// C++ program to find the area of Circumscribed  ``// circle of equilateral triangle ``#include ``#include ``const` `double` `pi = 3.14159265358979323846; `` ` `using` `namespace` `std; `` ` `// function to calculate the area of circumcircle ``// of equilateral triangle ``float` `area_circumscribed(``float` `a) ``{ ``    ``return` `(a * a * (pi / 3)); ``} ``// Driver code ``int` `main() ``{ ``    ``float` `a, Area; ``    ``a = 6; `` ` `    ``// function calling ``    ``Area = area_circumscribed(a); ``    ``// displaying the area ``    ``cout << ``"Area of CircumCircle :"` `<< Area; ``    ``return` `0; ``} `

## C

 `// C program to find the area of Circumscribed  ``// circle of equilateral triangle ``#include ``#define PI 3.14159265 `` ` `// function to find area of  ``// circumscribed circle ``float` `area_circumscribed(``float` `a) ``{ ``    ``return` `(a * a * (PI / 3)); ``} `` ` `// Driver code ``int` `main() ``{ ``    ``float` `a = 6; ``    ``printf``(``"Area of circumscribed circle is :%f"``, ``            ``area_circumscribed(a)); ``    ``return` `0; ``} `

## Java

 `// Java code to find the area of circumscribed  ``// circle of equilateral triangle ``import` `java.lang.*; `` ` `class` `GFG { ``     ` `    ``static` `double` `PI = ``3.14159265``; ``     ` `    ``// function to find the area of  ``    ``// circumscribed circle ``    ``public` `static` `double` `area_circumscribed(``double` `a) ``    ``{ ``        ``return` `(a * a * (PI / ``3``)); ``    ``} ``     ` `    ``// Driver code ``    ``public` `static` `void` `main(String[] args) ``    ``{ ``        ``double` `a = ``6.0``; ``        ``System.out.println(``"Area of circumscribed circle is :"` `                            ``+ area_circumscribed(a)); ``    ``} ``} `

## Python3

 `# Python3 code to find the area of circumscribed  ``# circle of equilateral triangle ``PI ``=` `3.14159265``     ` `# Function to find the area of  ``# circumscribed circle ``def` `area_circumscribed(a): ``    ``return` `(a ``*` `a ``*` `(PI ``/` `3``)) ``     ` `# Driver code ``a ``=` `6.0``print``(``"Area of circumscribed circle is :%f"``                        ``%``area_circumscribed(a)) `` ` `# This code is contributed by Anant Agarwal. `

## C#

 `// C# code to find the area of  ``// circumscribed circle ``// of equilateral triangle ``using` `System; `` ` `class` `GFG { ``    ``static` `double` `PI = 3.14159265; ``     ` `    ``// function to find the area of  ``    ``// circumscribed circle ``    ``public` `static` `double` `area_circumscribed(``double` `a) ``    ``{ ``        ``return` `(a * a * (PI / 3)); ``    ``} ``     ` `    ``// Driver code ``    ``public` `static` `void` `Main() ``    ``{ ``        ``double` `a = 6.0; ``        ``Console.Write(``"Area of circumscribed circle is :"` `+  ``                       ``area_circumscribed(a)); ``    ``} ``} `` ` `// This code is contributed by nitin mittal. `

## PHP

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## Javascript

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Output:
`Area of circumscribed circle is :37.6991118`

Time Complexity: O(1)
Auxiliary Space: O(1), since no extra space has been taken.

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