Area of a Triangle from the given lengths of medians

Namachila November 19, 2025

0 0 3 minutes read

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:

$Area (ABC) = \frac{4}{3} \sqrt{s(s-A)(s-B)(s-C)}$

where

$s = \frac{a+b+c}{2}$

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 <bits/stdc++.h> 
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

<script>
// javascript program to calculate 
// area of a triangle from the
// given lengths of medians
 
    // Function to return the area of
    // triangle using medians
    function Area_of_Triangle(a , b , c) {
        var s = (a + b + c) / 2;
        var x = s * (s - a);
        x = x * (s - b);
        x = x * (s - c);
        var area = (4 / 3) * Math.sqrt(x);
 
        return area;
    }
 
    // Driver Code
     
    var a = 9;
    var b = 12;
    var c = 15;
 
    // Function Call
    var ans = Area_of_Triangle(a, b, c);
 
    // Print the final answer
    document.write(ans.toFixed(1));
 
// This code is contributed by Rajput-Ji 
</script>

Output:

72.0

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

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