Área de un triángulo a partir de las longitudes dadas de las medianas

Dados tres números enteros A , B y C que denotan la longitud de las tres medianas de un triángulo, la tarea es calcular el área del triángulo.

La mediana de un triángulo es un segmento de recta que une un vértice con el punto medio del lado opuesto, bisecando así ese lado.

Ejemplos:

Entrada: A = 9, B = 12, C = 15 
Salida: 72,0
Entrada: A = 39, B = 42, C = 45 
Salida: 1008,0

Enfoque: 
el área del triángulo se puede calcular a partir de la longitud dada de las medianas usando la siguiente ecuación:

 

dónde 

 

A continuación se muestra la implementación del enfoque anterior:

// 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 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 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# 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

<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>

72.0

Tiempo Complejidad: O(1) 
Espacio Auxiliar: O(1)