怎么算面积——海伦公式：

S=sqrt(p(p-a)(p-b)(p-c));

p=(a+b+c)/2;

可是a,b,c都是边长，怎么算呢？

当然就用勾股定理啊！

代码：

#include <iostream>
#include <cmath>
using namespace std;
int main(){
	double x1,x2,x3,y1,y2,y3;
	cin>>x1>>y1>>x2>>y2>>x3>>y3;
	double a,b,c;
	a=sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
	b=sqrt((x2-x3)*(x2-x3)+(y2-y3)*(y2-y3));
	c=sqrt((x3-x1)*(x3-x1)+(y3-y1)*(y3-y1));
	double p=(a+b+c)/2;
	double S=sqrt(p*(p-a)*(p-b)*(p-c));
	printf("%.2f",S); 
	return 0;
}

#include <iostream>
#include <stdio.h>
#include <iomanip>
#include <math.h>
using namespace std;
const int N = 1e6 + 10;
const int INF = 0x3f3f3f3f;
int main()
{
	double a , b , c , d;
	float x1 , y1 , x2 , y2 , x3 , y3 , s;
	cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3;
	a = sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
	b = sqrt((x1 - x3) * (x1 - x3) + (y1 - y3) * (y1 - y3));
	c = sqrt((x3 - x2) * (x3 - x2) + (y3 - y2) * (y3 - y2));
	d = (a + b + c) / 2;
	s = sqrt(d * (d - a) * (d - b) * (d - c));
	cout << fixed << setprecision(2) << s;
	return 0;
}

#include <bits/stdc++.h>

using namespace std;

int main(void)
{
    double x1, y1;
    double x2, y2;
    double x3, y3;

	double m, n, e, p, s;

	cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3;

	m = sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
	n = sqrt((x1 - x3) * (x1 - x3) + (y1 - y3) * (y1 - y3));
	e = sqrt((x3 - x2) * (x3 - x2) + (y3 - y2) * (y3 - y2));
	p = (m + n + e) / 2;
	s = sqrt(p * (p - m) * (p - n) * (p - e));

	cout << fixed << setprecision(2) << s;

	return 0;
}

#include <stdio.h>
#include <iostream>
#include <math.h>
using namespace std;
int main()
{
	double x1,x2,x3,y1,y2,y3;
	double a, b, c, p, s;
	cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3;
	a = sqrt( (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
	b = sqrt( (x1 - x3) * (x1 - x3) + (y1 - y3) * (y1 - y3));
	c = sqrt( (x3 - x2) * (x3 - x2) + (y3 - y2) * (y3 - y2));
	p = (a + b + c) / 2;
	s = sqrt(p * (p - a) * (p - b) * (p -c));
	printf("%.2lf",s);
}

#include <stdio.h>
#include <iostream>
#include <math.h>
#include <iomanip>
using namespace std;
int main()
{
	double x1,y1,x2,y2,x3,y3;
	double a, b, c, p, s;
	cin >>x1>>y1>>x2>>y2>>x3>>y3;
	a=sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
	b=sqrt((x1-x3)*(x1-x3)+(y1-y3)*(y1-y3));
	c=sqrt((x3-x2)*(x3-x2)+(y3-y2)*(y3-y2));
	p=(a+b+c)/2;
	s=sqrt(p*(p-a)*(p-b)*(p-c));
	printf ("%.2lf\n",s);
}

#include <stdio.h>
#include <iostream>
#include <math.h>
#include <iomanip>
using namespace std;
int main()
{
	double x1,y1,x2,y2,x3,y3;
	double a, b, c, p, s;
	cin >>x1>>y1>>x2>>y2>>x3>>y3;
	a=sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
	b=sqrt((x1-x3)*(x1-x3)+(y1-y3)*(y1-y3));
	c=sqrt((x3-x2)*(x3-x2)+(y3-y2)*(y3-y2));
	p=(a+b+c)/2;
	s=sqrt(p*(p-a)*(p-b)*(p-c));
	printf ("%.2lf\n",s);
}

#include <stdio.h> #include <math.h> #include <iostream> using namespace std; int main() { double x1,x2,x3,y1,y2,y3; cin >>x1>> y1 >>x2>>y2>>x3>>y3; double a,b,c; a = sqrt( (x1 - x2)(x1 - x2) + (y1-y2)(y1-y2) ); b = sqrt( (x1 - x3)(x1 - x3) + (y1-y3)(y1-y3) ); c = sqrt( (x3 - x2)(x3 - x2) + (y3-y2)(y3-y2) ); double p = (a + b + c)/2; double s = sqrt( p * (p-a) * (p-b) * (p-c)); printf("%.2lf\n",s); }

#include <stdio.h> #include <iostream> #include <math.h> using namespace std; int main() { double x1,x2,x3,y1,y2,y3; double a, b, c, p, s; cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3; a = sqrt( (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); b = sqrt( (x1 - x3) * (x1 - x3) + (y1 - y3) * (y1 - y3)); c = sqrt( (x3 - x2) * (x3 - x2) + (y3 - y2) * (y3 - y2)); p = (a + b + c) / 2; s = sqrt(p * (p - a) * (p - b) * (p -c)); printf("%.2lf",s); }