杭电OJ -- 2036 改革春风吹满地

//任意多边形的面积计算

#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;

typedef std::pair<double ,double> point;

#pragma warning(disable:4244)

double det(point p0,point p1,point p2)
{
	return (p1.first-p0.first)*(p2.second-p0.second)-(p1.second-p0.second)*(p2.first-p0.first);
}

double ploygon_area(int n,point p[])
{
	double s=0.0f;
	int i=1;
	for(;i < n-1;i++)
		s += det(p[0],p[i],p[i+1]);
	return 0.5*fabs(s);
}

int main()
{

	int i,n;
	double s;
	point p_xy[101];
	while(cin >> n && n != 0)
	{

		for(i=0; i<n; i++){
			//cout<<endl<<"points["<<i<<"]=";
			cin>>p_xy[i].first>>p_xy[i].second;
		}

		s=ploygon_area(n, p_xy);
		cout << setiosflags(ios::fixed);
		cout.precision(1);
		cout << s << std::endl;
	}

	return 0;
}

http://blog.csdn.net/hemmingway/article/details/7814494 ---->要了解原理的请看这里。