Area of a non-convex polygon

Problem: A polygon (not necessarily convex) is defined on the plane by listing the coordinates of the vertices in the order of traversing its boundary. Determine the area of the polygon.

I wrote code to calculate the area of a convex polygon (yes, with heap memory allocation). How can it be modified to calculate the area of a non-convex polygon and in general the algorithm for determining whether the entered polygon is convex or not? (If without splitting the polygon into shapes if not, then please write how to break it up and calculate each shape separately)

#include "stdafx.h"
#include <iostream>

using namespace System;
using namespace std;

int main()
{
    setlocale(0, "");
    int y, x, c, i = 0;
    cout << "Кол-во углов ";
    cin >> c;
    int(*coor)[2];
    coor = new int[c][2];
    while (i != c)
    {
        for (int j = 0; j < 2; j++)
        {
            cout << "Введите координаты " << endl;
            cout << "По X ";
            cin >> x;
            cout << "По Y ";
            cin >> y;
            coor[i][j] = x;
            j = 1;
            coor[i][j] = y;
            j = 2;
        }
        i++;
    };
    i = 0;
    int t = i + 1;
    double sum, pl = 0;
    for (i; t!= c; i++)
    {
        sum = ((coor[i][0] + coor[t][0])*(coor[i][1] - coor[t][1])) / 2;
        pl = pl + sum;
        t++;
    }
    cout << "Площадь " << abs(pl) << endl;
    system("pause");
    delete[]coor;
}

This is how the same program looks without arrays. Everything works right here. Apparently, I integrated the dynamic array here incorrectly... Please help me

int n, x, y, x1, x2, y1, y2;
    double sum = 0;
    cout << "Введите кол-во углов многоугольника: ";
    cin >> n;
    cout << "Введите координаты вершины многоугольника: ";
    cin >> x >> y;
    x1 = x;
    y1 = y;
    for (int i = 0; i < (n - 1); i++) 
    {
        cout << "Введите координаты следующей вершины: ";
        cin >> x2 >> y2;
        sum = sum + (x1 + x2)*(y2 - y1);
        x1 = x2;
        y1 = y2;
    }
    sum = sum + (x + x2)*(y - y2);
    sum = abs(sum) / 2;
    cout << fixed << setprecision(3) << sum << endl;