[LivingNightmare]

Description: Function That Calculates The Area Of A Polygon Given It's Vertices. This Uses The The Shoelace Algorithm. For More Information: http://en.wikipedia....hoelace_formula

/************************************************
Program that calculates the area of a polygon
given it's vertices in the XY plane.
This program uses an algorithm known as the
shoelace algorithm. For more information,
see the wikipedia link:
http://en.wikipedia.org/wiki/Shoelace_algorithm
*************************************************/

#include <iostream>
#include <vector>
using namespace std;

// Function that calculates the absolute value
// of a double type.
double MyAbs(double num)
{
    double inv = num * -1;
    return (num <= 0) ? inv : num;
}

// Function that calculates the area given a
// vector of vertices in the XY plane.
double CalcArea(vector< pair<double, double> > list)
{
    double area = 0; // Total Area
    double diff = 0; // Difference Of Y{i + 1} - Y{i - 1}
    unsigned int last = list.size() - 1; // Size Of Vector - 1

    /* Given vertices from 1 to n, we first loop through
    the vertices 2 to n - 1. We will take into account
    vertex 1 and vertex n sepereately */
    for(unsigned int i = 1; i < last; i++)
    {
        diff =list[i + 1].second - list[i - 1].second;
        area += list[i].first * diff;
    }

    /* Now We Consider The Vertex 1 And The Vertex N */
    diff = list[1].second - list[last].second;
    area += list[0].first * diff; // Vertex 1

    diff = list[0].second - list[last - 1].second;
    area += list[last].first * diff; // Vertex N

    /* Calculate The Final Answer */
    area = 0.5 * MyAbs(area);
    return area; // Return The Area
}

/* Main Function - Sample */
int main()
{
    unsigned int vertex = 0;
    double x = 0;
    double y = 0;

    vector< pair<double, double> > v;

    cout<<"Enter A Valid Number Of Vertices: " <<endl;
    cin >> vertex;
    cout<< endl;

    while(vertex > 0) {
        cout<<"Enter Pair X Y: ";
        cin >> x >> y;
        v.push_back(make_pair(x, y));
        vertex--;
    }

    cout<<"The Area Of The Polygon Is: " << CalcArea(v) <<endl;
    return 0;
}

[KYA]

A little brittle. Vertices must be entered in the correct order (i.e. linearly as on the graph).