# 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
```

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

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 Cicumscribed  ` `// 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 Cicumscribed  ` `// 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_cicumscribed(``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_cicumscribed(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_cicumscribed(a): ` `    ``return` `(a ``*` `a ``*` `(PI ``/` `3``)) ` `     `  `# Driver code ` `a ``=` `6.0` `print``(``"Area of circumscribed circle is :%f"` `                        ``%``area_cicumscribed(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_cicumscribed(``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_cicumscribed(a)); ` `    ``} ` `} ` ` `  `// This code is contributed by nitin mittal. `

## PHP

 ` `

Output:

```Area of circumscribed circle is :37.6991118
```