Area of the circumcircle of any triangles with sides given - GeeksforGeeks

11 Nov, 2021
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: 



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++
Java
Python3
C#
PHP
Javascript
// 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 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 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 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# 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// PHP Program to find the// area the circumcircle of// the given triangle // Function to find the area// of the circumcirclefunction 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; $c = 3; // Find and print the area// of the circumcircleecho circlearea($a, $b, $c); // This code is contributed// by inder_verma?>
<script>// javascript Program to find the area// the circumcircle of the given triangle // Function to find the area// of the circumcirclefunction 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 trianglevar a = 4, b = 5, c = 3; // Find and print the area of the circumcircledocument.write(circlearea(a, b, c)); // This code contributed by Princi Singh </script>
19.625
 
SoumikMondal
Shashank12
inderDuMCA
Shivi_Aggarwal
divyanshsinghxi
princi singh
Kirti_Mangal
circle
triangle
Geometric
School Programming
Geometric
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