# C++ Program to implement Slicker Algorithm that avoids Triangulation to find Area of a Polygon

Here is a C++ program to find the area of polygon using slicker algorithm that avoids Triangulation to find area of a polygon.

It assumes the usual mathematical convention that positive y points upwards. In computer systems where positive y is downward, the easiest thing to do is to list the vertices counter-clockwise using the “positive y down” coordinates. Two effects then canceled out to produce a positive area.

## Algorithm

Begin
function Area() is used to calculate area of a polygon take the polygon p as argument.
for i = 0 to p.n-1
initialize j = (i + 1) % p.n;
calculate t =t+((p.p[i].b * p.p[j].b) - (p.p[j].a * p.p[i].b.))
return t/2
End

## Example Code

#include <iostream>
using namespace std;

const int MAX = 200;
class P// to declare variables {
private:
public:
double a, b;
};

class Polygon {
private:
public:
P p[MAX];
int n;

Polygon()//take the coordinates of each point of polygon {
for (int i = 0; i < MAX; i++)
P p[i];
}
};

double Area(Polygon p)//area calculation {
double t = 0;
for (int i = 0; i < p.n; i++) {
int j = (i + 1) % p.n;
t += (p.p[i].b * p.p[j].b) - (p.p[j].a * p.p[i].b);
}
return t / 2;
}

int main(int argc, char **argv) {
Polygon p;

cout << "Enter the number of points in Polygon: ";
cin >>p.n;
cout << "Enter the coordinates of each point: ";
for (int i = 0; i < p.n; i++) {
cin >>p.p[i].a;
cin >>p.p[i].b;
}

double a = Area(p);
if (a >0)//if area>0
cout << "The Area of Polygon with " << p.n
<< " points using Slicker Algorithm is : " << a;
else
cout << "The Area of Polygon with " << p.n
<< " points using Slicker Algorithm is : " << (a * -1);
}

## Output

Enter the number of points in Polygon: 6
Enter the coordinates of each point:
1 1
2 2
3 3
4 4
5 5
6 7
The Area of Polygon with 6 points using Slicker Algorithm is : 2.5