叉乘

#include <bits/stdc++.h>
using namespace std;
int main()
{
    double xa, ya, xb, yb, xc, yc;
    cin >> xa >> ya >> xb >> yb >> xc >> yc;
    double x = xc - xa, y = yc - ya;
    double xx = xb - xa, yy = yb - ya;
    double ans = (x * yy - y * xx) / 2;
    if (ans < 0)
        ans = -ans;
    cout << fixed << setprecision(2) << ans;
    return 0;
}

海伦公式

#include<bits/stdc++.h>
using namespace std;
int main(){
	double x,y,xx,yy,xxx,yyy;
	cin>>x>>y>>xx>>yy>>xxx>>yyy;
	double len1=sqrt((x-xx)*(x-xx)+(y-yy)*(y-yy));
	double len2=sqrt((x-xxx)*(x-xxx)+(y-yyy)*(y-yyy));
	double len3=sqrt((xxx-xx)*(xxx-xx)+(yyy-yy)*(yyy-yy));
	double p=(len1+len2+len3)/2;
	double s=sqrt(p*(p-len1)*(p-len2)*(p-len3));
	cout<<fixed<<setprecision(2)<<s<<endl;
	return 0;
}