using System;

using System.Collections.Generic;

​

public class Program

{

    public static void Main()

    {

        IList<LatLng> path = new List<LatLng>();

        path.Add(new LatLng(-20.253605204701, -70.106903276165));

        path.Add(new LatLng(-20.253818617830, -70.107765556612));

        path.Add(new LatLng(-20.254495614967, -70.107654186777));

        path.Add(new LatLng(-20.254400336391, -70.106938131964));

        var resultado = SphericalUtil.ComputeSignedArea(path);

        Console.WriteLine("Hello World " + resultado);

    }

}

​

public static class SphericalUtil

{

    const double EARTH_RADIUS = 6371009;

​

    static double ToRadians(double input)

    {

        return input / 180.0 * Math.PI;

    }

​

    public static double ComputeSignedArea(IList<LatLng> path)

    {

        return ComputeSignedArea(path, EARTH_RADIUS);

    }

​

    static double ComputeSignedArea(IList<LatLng> path, double radius)

    {

        int size = path.Count;

        if (size < 3) { return 0; }

        double total = 0;

        var prev = path[size - 1];

        double prevTanLat = Math.Tan((Math.PI / 2 - ToRadians(prev.Latitude)) / 2);

        double prevLng = ToRadians(prev.Longitude);

​

        foreach (var point in path)

        {

            double tanLat = Math.Tan((Math.PI / 2 - ToRadians(point.Latitude)) / 2);

            double lng = ToRadians(point.Longitude);

            total += PolarTriangleArea(tanLat, lng, prevTanLat, prevLng);

            prevTanLat = tanLat;

            prevLng = lng;

        }

        return total * (radius * radius);

    }

​

    static double PolarTriangleArea(double tan1, double lng1, double tan2, double lng2)

    {

        double deltaLng = lng1 - lng2;

        double t = tan1 * tan2;

        return 2 * Math.Atan2(t * Math.Sin(deltaLng), 1 + t * Math.Cos(deltaLng));

    }

}

​

public class LatLng

{

    public double Latitude {get;set;}

    public double Longitude {get;set;}

    public LatLng(double latitude, double longitude)

    {

        this.Latitude = latitude;

        this.Longitude = longitude;

    }

}