# 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:114.834Input:a = 4, b = 5, c = 3Output:314

**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) / 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; ` `} ` |

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## 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) / 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.. ` |

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## 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) ` `/` `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` `(` `int` `(circlearea(a, b, c))); ` `print` `(` `"\n"` `); ` ` ` `# This code is contributed ` `# by Shivi_Aggarwal ` |

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## 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) / 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 ` |

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## 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` `) / ` `$At` `), 2); ` ` ` `return` `$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 os contributed ` `// by inder_verma ` `?> ` |

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**Output:**

314

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