double Area( 
   Geometry geometry
)

var g1 = PolygonBuilder.FromJson("{\"rings\": [ [ [0, 0], [10, 0], [10, 10], [0, 10] ] ] }");
double d = GeometryEngine.Instance.Area(g1);
// d = -100.0         //negative due to wrong ring orientation
d = GeometryEngine.Instance.Area(GeometryEngine.Instance.SimplifyAsFeature(g1));
// d = 100.0        // feature has been simplifed; ring orientation is correct

List<Coordinate2D> outerCoordinates = new List<Coordinate2D>();
outerCoordinates.Add(new Coordinate2D(10.0, 10.0));
outerCoordinates.Add(new Coordinate2D(10.0, 20.0));
outerCoordinates.Add(new Coordinate2D(20.0, 20.0));
outerCoordinates.Add(new Coordinate2D(20.0, 10.0));

// Builder constructors need to run on the MCT.
ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
{
  // use the PolygonBuilder as we wish to manipulate the parts
  using (PolygonBuilder pb = new PolygonBuilder(outerCoordinates))
  {
    Polygon donut = pb.ToGeometry();
    double area = donut.Area;       // area = 100

    // define the inner polygon as anti-clockwise
    List<Coordinate2D> innerCoordinates = new List<Coordinate2D>();
    innerCoordinates.Add(new Coordinate2D(13.0, 13.0));
    innerCoordinates.Add(new Coordinate2D(17.0, 13.0));
    innerCoordinates.Add(new Coordinate2D(17.0, 17.0));
    innerCoordinates.Add(new Coordinate2D(13.0, 17.0));

    pb.AddPart(innerCoordinates);
    donut = pb.ToGeometry();

    area = donut.Area;    // area = 84.0

    area = GeometryEngine.Instance.Area(donut);    // area = 84.0
  }
});