海伦公式

/*
海伦公式：给三条边abc就可以计算三角形面积S
    p = (a+b+c)/2
    S = sqrt( p*[p-a]*[p-b]*[p-c] )

别问为什么写的这么啰嗦，问就是降低理解难度
*/
#include <iostream>
#include <algorithm>
#include <cmath>
using namespace std;

typedef pair<double, double> P;
#define x first
#define y second

int main()
{
    P pts[3];
    for (int i = 0; i < 3; i++)
        cin >> pts[i].x >> pts[i].y;

    int k = 0;
    double line[3];  // 记录三条边长度

    for (int i = 0; i < 3; i++)
    {
        for (int j = i + 1; j < 3; j++)  // 枚举三条边
        {
            double x1 = pts[i].x;
            double y1 = pts[i].y;

            double x2 = pts[j].x;
            double y2 = pts[j].y;

            double dx = x1 - x2;
            double dy = y1 - y2;

            line[k++] = sqrt(dx * dx + dy * dy);  // 欧氏距离
        }
    }

    double a = line[0];
    double b = line[1];
    double c = line[2];
    double p = (a + b + c) / 2;

    double res = sqrt(p * (p - a) * (p - b) * (p - c));
    printf("%.03lf\n", res);

    return 0;
}

向量的叉积

/*
向量的叉积：
S = 1/2(ab * bc)  ab,bc指任意两边的向量，默认012-abc边
*/
#include <iostream>
#include <algorithm>
#include <cmath>
using namespace std;

typedef pair<double, double> P;
#define x first
#define y second

// 计算ab，bc的叉积
double cross(double x1, double y1, double x2, double y2)
{
    double res = x1 * y2 - x2 * y1;
    return res;
}

int main()
{
    P pts[3];
    for (int i = 0; i < 3; i++)
        cin >> pts[i].x >> pts[i].y;

    P vector[2];  // 存储向量ab,bc
    vector[0].x = pts[0].x - pts[1].x;
    vector[0].y = pts[0].y - pts[1].y;

    vector[1].x = pts[1].x - pts[2].x;
    vector[1].y = pts[1].y - pts[2].y;

    double res = 0.5 * cross(vector[0].x, vector[0].y, vector[1].x, vector[1].y);
    printf("%.03lf\n", res);

    return 0;
}