# Area of the circumcircle of any triangles with sides given

• Last Updated : 27 Aug, 2022

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: 7.17714

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

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

Radius of the circumcircle:
[Tex]= \frac{abc}{4\sqrt{\left ( s\left ( a+b-s \right )\left ( a+c-s \right )\left ( b+c-s \right ) \right )}}[/Tex]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 circumcirclefloat 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 codeint 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 triangleimport java.*;class gfg{// Function to find the area// of the circumcirclepublic 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 codepublic 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 triangleimport math # Function to find the area# of the circumcircledef 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 trianglea = 4;b = 5;c = 3; # Find and print the area# of the circumcircleprint (float(circlearea(a, b, c))); # This code is contributed# by Shivi_Aggarwal

## C#

 // C# Program to find the area// the circumcircle of the given triangleusing 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

 

## Javascript

 

Output

19.625

Time Complexity: O(log(n)) as it is using inbuilt sqrt function
Auxiliary Space: O(1)

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