//* Grouping data in classes *
#include <iostream>
#include <cmath>
using namespace std;

class Point {
public:
    double x, y;
};

double sqr(double x);
double DIST(Point a, Point b);
double AREA(double a, double b, double c);
double TRIA(Point x, Point y, Point z);

int main() {
    cout << "Please enter the coordinates of the triangle vertices and press ENTER." << endl;
    Point p1, p2, p3;
    cin >> p1.x >> p1.y >> p2.x >> p2.y >> p3.x >> p3.y;
    double area=TRIA(p1, p2, p3);
    cout << "The area of the triangle is " << area << endl;
    return(0);
}

double sqr(double x) {
    return(x*x);
}

double DIST(Point a, Point b) {
    return( sqrt( sqr(a.x-b.x)+sqr(a.y-b.y) ) );
}

double AREA(double a, double b, double c) {
    // Hero's formula for the triangle area
    double p=(a+b+c)/2.0;
    double ar=sqrt(p*(p-a)*(p-b)*(p-c));
    return(ar);
}

double TRIA(Point x, Point y, Point z) {
    double leg1=DIST(x,y);
    double leg2=DIST(x,z);
    double leg3=DIST(y,z);
    double area=AREA(leg1, leg2, leg3);
    return(area);
}