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*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 = π*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)/ √3.

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

`// C++ program to find the area of Cicumscribed ` `// 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; `
`} ` |

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`// C program to find the area of Cicumscribed ` `// 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; `
`} ` |

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`// 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)); `
` ` `} `
`} ` |

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`# 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. ` |

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`// 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. ` |

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`<?php ` `// PHP program to find the ` `// area of Cicumscribed ` `// 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. ` `?> ` |

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**Output:**

Area of circumscribed circle is :37.6991118

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