给定中线长度的三角形面积

给定三个整数A 、 B和C ，它们表示三角形的三个中线的长度，任务是计算三角形的面积。

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

例子：

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

方法：
三角形的面积可以使用以下等式从给定的中线长度计算：

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

where 

$s = \frac{a+b+c}{2}$
 

下面是上述方法的实现：

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

// 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);
 
    // Prvar the final answer
    document.write(ans.toFixed(1));
 
// This code is contributed by Rajput-Ji

输出：

72.0

时间复杂度： O(1)
辅助空间： O(1)