public sealed class Polygon : Multipart 

/// <summary>
/// The methods retrieves the outer ring(s) of the input polygon.
/// </summary>
/// <param name="inputPolygon">Input Polygon.</param>
/// <returns>The outer most (exterior, clockwise) ring(s) of the polygon. If the input is null or empty, a null pointer is returned.</returns>
public Polygon GetOutermostRings(Polygon inputPolygon)
{
  if (inputPolygon == null || inputPolygon.IsEmpty)
    return null;

  List<Polygon> internalRings = new List<Polygon>();

  // explode the parts of the polygon into a list of individual geometries
  // see the "Get the individual parts of a multipart feature"
  // snippet for MultipartToSinglePart
  var parts = MultipartToSinglePart(inputPolygon);

  // get an enumeration of clockwise geometries (area > 0) ordered by the area
  var clockwiseParts = parts.Where(geom => ((Polygon)geom).Area > 0)
                        .OrderByDescending(geom => ((Polygon)geom).Area);

  // for each of the exterior rings
  foreach (var part in clockwiseParts)
  {
    // add the first (the largest) ring into the internal collection
    if (internalRings.Count == 0)
      internalRings.Add(part as Polygon);

    // use flag to indicate if current part is within the already selection polygons
    bool isWithin = false;

    foreach (var item in internalRings)
    {
      if (GeometryEngine.Instance.Within(part, item))
        isWithin = true;
    }

    // if the current polygon is not within any polygon of the internal collection
    // then it is disjoint and needs to be added to 
    if (isWithin == false)
      internalRings.Add(part as Polygon);
  }

  PolygonBuilderEx outerRings = new PolygonBuilderEx();
  // now assemble a new polygon geometry based on the internal polygon collection
  foreach (var ring in internalRings)
  {
    outerRings.AddParts(ring.Parts);
  }

  // return the final geometry of the outer rings
  return outerRings.ToGeometry();
}

// methods need to run on the MCT
ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
{
  try
  {
    // open a gdb
    using (ArcGIS.Core.Data.Geodatabase gdb = 
              new ArcGIS.Core.Data.Geodatabase(
                  new FileGeodatabaseConnectionPath(new Uri(@"c:\Temp\MyDatabase.gdb"))))
    {
      //Open a featureClass 
      using (ArcGIS.Core.Data.FeatureClass featureClass = 
                     gdb.OpenDataset<ArcGIS.Core.Data.FeatureClass>("Polygon"))
      {
        
        ArcGIS.Core.Data.QueryFilter filter = 
                   new ArcGIS.Core.Data.QueryFilter()
                    {
                      WhereClause = "OBJECTID = 6"
                    };

        // get the row
        using (ArcGIS.Core.Data.RowCursor rowCursor = 
                               featureClass.Search(filter, false))
        {
          while (rowCursor.MoveNext())
          {
            using (var row = rowCursor.Current)
            {
              long oid = row.GetObjectID();

              // get the shape from the row
              ArcGIS.Core.Data.Feature feature = row as ArcGIS.Core.Data.Feature;
              Polygon polygon = feature.GetShape() as Polygon;

              // do something here
            }
          }
        }
      }
    }
  }
  catch (Exception ex)
  {
    // error - handle appropriately
  }
});