# 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 = 3
Output: 114.834

Input: a = 4, b = 5, c = 3
Output: 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  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;  }

## 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..

## 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

## 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

## PHP

 

Output:

314


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