# Area of the circumcircle of any triangles with sides given

Given a triangle with known sides a, b and c; the task is to find the area of its circumcircle.**Examples:**

Input:a = 2, b = 2, c = 3Output:7.17714Input:a = 4, b = 5, c = 3Output:19.625

**Approach:**

For a triangle with side lengths a, b, and c,

Radius of the circumcircle:where A = √(s*(s-a)*(s-b)*(s-c)) and s = (a+b+c)/2 is the semiperimeter.Therefore, Area of the circumcircle:

Below is the implementation of the above approach:

## C++

`// C++ Program to find the area` `// the circumcircle of the given triangle` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the area` `// of the circumcircle` `float` `circlearea(` `float` `a, ` `float` `b, ` `float` `c)` `{` ` ` `// the sides cannot be negative` ` ` `if` `(a < 0 || b < 0 || c < 0)` ` ` `return` `-1;` ` ` `// semi-perimeter of the circle` ` ` `float` `p = (a + b + c) / 2;` ` ` `// area of triangle` ` ` `float` `At = ` `sqrt` `(p * (p - a) * (p - b) * (p - c));` ` ` `// area of the circle` ` ` `float` `A = 3.14 * ` `pow` `(((a * b * c) / (4 * At)), 2);` ` ` `return` `A;` `}` `// Driver code` `int` `main()` `{` ` ` `// Get the sides of the triangle` ` ` `float` `a = 4, b = 5, c = 3;` ` ` `// Find and print the area of the circumcircle` ` ` `cout << circlearea(a, b, c) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java Program to find the area` `// the circumcircle of the given triangle` `import` `java.*;` `class` `gfg` `{` `// Function to find the area` `// of the circumcircle` `public` `double` `circlearea(` `double` `a, ` `double` `b, ` `double` `c)` `{` ` ` `// the sides cannot be negative` ` ` `if` `(a < ` `0` `|| b < ` `0` `|| c < ` `0` `)` ` ` `return` `-` `1` `;` ` ` `// semi-perimeter of the circle` ` ` `double` `p = (a + b + c) / ` `2` `;` ` ` `// area of triangle` ` ` `double` `At = Math.sqrt(p * (p - a) * (p - b) * (p - c));` ` ` `// area of the circle` ` ` `double` `A = ` `3.14` `* Math.pow(((a * b * c) / (` `4` `* At)), ` `2` `);` ` ` `return` `A;` `}` `}` `class` `geek` `{` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `gfg g = ` `new` `gfg();` ` ` `// Get the sides of the triangle` ` ` `double` `a = ` `4` `, b = ` `5` `, c = ` `3` `;` ` ` `// Find and print the area of the circumcircle` ` ` `System.out.println(g.circlearea(a, b, c));` `}` `}` `//This code is contributed by shk..` |

## Python3

`# Python3 Program to find the area` `# the circumcircle of the given triangle` `import` `math` `# Function to find the area` `# of the circumcircle` `def` `circlearea(a, b, c):` ` ` `# the sides cannot be negative` ` ` `if` `(a < ` `0` `or` `b < ` `0` `or` `c < ` `0` `):` ` ` `return` `-` `1` `;` ` ` `# semi-perimeter of the circle` ` ` `p ` `=` `(a ` `+` `b ` `+` `c) ` `/` `2` `;` ` ` `# area of triangle` ` ` `At ` `=` `math.sqrt(p ` `*` `(p ` `-` `a) ` `*` ` ` `(p ` `-` `b) ` `*` `(p ` `-` `c));` ` ` `# area of the circle` ` ` `A ` `=` `3.14` `*` `pow` `(((a ` `*` `b ` `*` `c) ` `/` `(` `4` `*` `At)), ` `2` `);` ` ` `return` `A;` `# Driver code` `# Get the sides of the triangle` `a ` `=` `4` `;` `b ` `=` `5` `;` `c ` `=` `3` `;` `# Find and print the area` `# of the circumcircle` `print` `(` `float` `(circlearea(a, b, c)));` `# This code is contributed` `# by Shivi_Aggarwal` |

## C#

`// C# Program to find the area` `// the circumcircle of the given triangle` `using` `System;` `class` `gfg` `{` ` ` `// Function to find the area` ` ` `// of the circumcircle` ` ` `public` `double` `circlearea(` `double` `a, ` `double` `b, ` `double` `c)` ` ` `{` ` ` `// the sides cannot be negative` ` ` `if` `(a < 0 || b < 0 || c < 0)` ` ` `return` `-1;` ` ` `// semi-perimeter of the circle` ` ` `double` `p = (a + b + c) / 2;` ` ` `// area of triangle` ` ` `double` `At = Math.Sqrt(p * (p - a) * (p - b) * (p - c));` ` ` `// area of the circle` ` ` `double` `A = 3.14 * Math.Pow(((a * b * c) / (4 * At)), 2);` ` ` `return` `A;` ` ` `}` `}` `class` `geek` `{` ` ` `// Driver code` ` ` `public` `static` `int` `Main()` ` ` `{` ` ` `gfg g = ` `new` `gfg();` ` ` `// Get the sides of the triangle` ` ` `double` `a = 4, b = 5, c = 3;` ` ` `// Find and print the area of the circumcircle` ` ` `Console.WriteLine(g.circlearea(a, b, c));` ` ` `return` `0;` ` ` `}` `}` `//This code os contributed by SoumikMondal` |

## PHP

`<?php` `// PHP Program to find the` `// area the circumcircle of` `// the given triangle` `// Function to find the area` `// of the circumcircle` `function` `circlearea(` `$a` `, ` `$b` `, ` `$c` `)` `{` ` ` `// the sides cannot be negative` ` ` `if` `(` `$a` `< 0 || ` `$b` `< 0 || ` `$c` `< 0)` ` ` `return` `-1;` ` ` `// semi-perimeter of the circle` ` ` `$p` `= (` `$a` `+ ` `$b` `+ ` `$c` `) / 2;` ` ` `// area of triangle` ` ` `$At` `= sqrt(` `$p` `* (` `$p` `- ` `$a` `) *` ` ` `(` `$p` `- ` `$b` `) * (` `$p` `- ` `$c` `));` ` ` `// area of the circle` ` ` `$A` `= 3.14 * pow(((` `$a` `* ` `$b` `*` ` ` `$c` `) / (4 * ` `$At` `)), 2);` ` ` `return` `$A` `;` `}` `// Driver code` `// Get the sides of the triangle` `$a` `= 4; ` `$b` `= 5; ` `$c` `= 3;` `// Find and print the area` `// of the circumcircle` `echo` `circlearea(` `$a` `, ` `$b` `, ` `$c` `);` `// This code is contributed` `// by inder_verma` `?>` |

## Javascript

`<script>` `// javascript Program to find the area` `// the circumcircle of the given triangle` `// Function to find the area` `// of the circumcircle` `function` `circlearea(a , b , c)` `{` ` ` `// the sides cannot be negative` ` ` `if` `(a < 0 || b < 0 || c < 0)` ` ` `return` `-1;` ` ` `// semi-perimeter of the circle` ` ` `var` `p = (a + b + c) / 2;` ` ` `// area of triangle` ` ` `var` `At = Math.sqrt(p * (p - a) * (p - b) * (p - c));` ` ` `// area of the circle` ` ` `var` `A = 3.14 * Math.pow(((a * b * c) / (4 * At)), 2);` ` ` `return` `A;` `}` `// Driver code` `// Get the sides of the triangle` `var` `a = 4, b = 5, c = 3;` `// Find and print the area of the circumcircle` `document.write(circlearea(a, b, c));` `// This code contributed by Princi Singh` `</script>` |

**Output:**

19.625