# 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 / âˆš3), 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:

(Ï€*a^{2)/3}

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

**How this formulae works?**

We know that area of circle = Ï€*r^{2}, where r is the radius of given circle.

We also know that radius of Circumcircle of an equilateral triangle = (side of the equilateral triangle)/ âˆš3.

Therefore, area = Ï€*r^{2} = Ï€*a^{2}/3.

## C++

`// C++ program to find the area of Circumscribed ` `// circle of equilateral triangle` `#include <iostream>` `#include <math.h>` `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 <stdio.h>` `#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

`<?php` `// PHP program to find the ` `// area of Circumscribed ` `// circle of equilateral triangle` `$PI` `= 3.14159265;` `// function to find area of ` `// circumscribed circle` `function` `area_circumscribed(` `$a` `)` `{` ` ` `global` `$PI` `;` ` ` `return` `(` `$a` `* ` `$a` `* (` `$PI` `/ 3));` `}` `// Driver code` `$a` `= 6;` `echo` `(` `"Area of circumscribed circle is :"` `);` `echo` `(area_circumscribed(` `$a` `));` `// This code is contributed by Ajit.` `?>` |

## Javascript

`<script>` `// javascript program to find the area of Circumscribed ` `// circle of equilateral triangle` `let pi = 3.14159265358979323846;` `// function to calculate the area of circumcircle` `// of equilateral triangle` `function` `area_circumscribed( a)` `{` ` ` `return` `(a * a * (pi / 3));` `}` `// Driver code` ` ` `let a, Area;` ` ` `a = 6;` ` ` `// function calling` ` ` `Area = area_circumscribed(a);` ` ` `// displaying the area` ` ` `document.write(` `"Area of CircumCircle :"` `+ Area.toFixed(7));` `// This code is contributed by todaysgaurav` `</script>` |

**Output:**

Area of circumscribed circle is :37.6991118

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