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#include <iostream>
#include <math.h>
using namespace std;
double calcArea(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4, double x5, double y5);
double calcLength(double x1, double y1, double x2, double y2);
int main()
{
double x1, y1, x2, y2, x3, y3, x4, y4, x5, y5;
cout << "Enter the cooordinates of the 5 vertices of a pentagon:\n";
cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3 >> x4 >> y4 >> x5 >> y5;
double a = calcArea(x1, y1, x2, y2, x3, y3, x4, y4, x5, y5);
cout << "The pentagons area is = " << a << "\n";
system ("pause");
return 0;
}
double calcArea(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4, double x5, double y5)
{
double L1 = calcLength(x1, y1, x2, y2);
double L2 = calcLength(x1, y1, x3, y3);
double L3 = calcLength(x2, y2, x3, y3);
double L4 = calcLength(x1, y1, x5, y5);
double L5 = calcLength(x3, y3, x5, y5);
double L6 = calcLength(x4, y4, x5, y5);
double L7 = calcLength(x3, y3, x4, y4);
double s = (L1 + L2 + L3)/2;
double s2 = (L2 + L4 + L5)/2;
double s3 = (L5 + L6 + L7)/2;
return (sqrt(s*(s-L1)*(s-L2)*(s-L3))+ sqrt(s2*(s-L2)*(s-L4)*(s-L5))+ sqrt(s3*(s-L5)*(s-L6)*(s-L7)));
}
double calcLength(double x1, double y1, double x2, double y2)
{
return sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));
}
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