# Program to calculate area of Circumcircle of an Equilateral Triangle

• Difficulty Level : Basic
• Last Updated : 27 Aug, 2022

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:

`(π*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 = π*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 = π*r2 = π*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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