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# 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:

`(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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