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Area of a Triangle from the given lengths of medians

• Last Updated : 01 Feb, 2022

Given three integers A,B and C which denotes length of the three medians of a triangle, the task is to calculate the area of the triangle.

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side.

Examples:

Input: A = 9, B = 12, C = 15
Output: 72.0
Input: A = 39, B = 42, C = 45
Output: 1008.0

Approach:
The area of the triangle can be calculated from the given length of medians using the following equation:

where

Below is the implementation of the above approach:

C++14

 // C++14 program to calculate  // area of a triangle from the  // given lengths of medians  #include  using namespace std;    // Function to return the area of  // triangle using medians  double Area_of_Triangle(int a, int b, int c)  {      int s = (a + b + c) / 2;      int x = s * (s - a);      x = x * (s - b);      x = x * (s - c);      double area = (4 / (double)3) * sqrt(x);        return area;  }    // Driver Code  int main()  {      int a = 9;      int b = 12;      int c = 15;            // Function call      double ans = Area_of_Triangle(a, b, c);            // Print the final answer      cout << ans;  }   // This code is contributed by code_hunt

Java

 // Java program to calculate  // area of a triangle from the // given lengths of medians class GFG{   // Function to return the area of  // triangle using medians  static double Area_of_Triangle(int a,                                 int b, int c)  {      int s = (a + b + c)/2;     int x = s * (s - a);     x = x * (s - b);     x = x * (s - c);     double area = (4 / (double)3) * Math.sqrt(x);       return area; }   // Driver Code  public static void main(String[] args) {     int a = 9;     int b = 12;     int c = 15;           // Function Call      double ans = Area_of_Triangle(a, b, c);           // Print the final answer      System.out.println(ans); } }   // This code is contributed by sapnasingh4991

Python3

 # Python3 program to calculate  # area of a triangle from the # given lengths of medians import math    # Function to return the area of  # triangle using medians  def Area_of_Triangle(a, b, c):        s = (a + b + c)//2     x = s * (s - a)     x = x * (s - b)     x = x * (s - c)     area = (4 / 3) * math.sqrt(x)       return area   # Driver Code  a = 9 b = 12 c = 15   # Function Call  ans = Area_of_Triangle(a, b, c)    # Print the final answer  print(round(ans, 2))

C#

 // C# program to calculate  // area of a triangle from the // given lengths of medians using System;   class GFG{   // Function to return the area of  // triangle using medians  static double Area_of_Triangle(int a,                                 int b, int c)  {      int s = (a + b + c) / 2;     int x = s * (s - a);           x = x * (s - b);     x = x * (s - c);           double area = (4 / (double)3) * Math.Sqrt(x);       return area; }   // Driver Code  public static void Main(String[] args) {     int a = 9;     int b = 12;     int c = 15;           // Function call      double ans = Area_of_Triangle(a, b, c);           // Print the final answer      Console.WriteLine(ans); } }   // This code is contributed by sapnasingh4991

Javascript

 

Output:

72.0

Time Complexity: O(1)
Auxiliary Space: O(1)

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