public void SetShape( 
   Geometry shape
)

public async Task ModifyingAFeature()
{
  string message = String.Empty;
  bool modificationResult = false;

  await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
  {
    using (Geodatabase geodatabase = new Geodatabase(new DatabaseConnectionFile(new Uri("path\\to\\sde\\file\\sdefile.sde"))))
    using (FeatureClass enterpriseFeatureClass = geodatabase.OpenDataset<FeatureClass>("LocalGovernment.GDB.FacilitySite"))
    {

      //var geodatabase = new Geodatabase(new FileGeodatabaseConnectionPath(uri)) for a File GDB
      //
      //var shapeFileConnPath = new FileSystemConnectionPath(uri, FileSystemDatastoreType.Shapefile);
      //var shapefile = new FileSystemDatastore(shapeFileConnPath);
      //var table = shapefile.OpenDataset<Table>(strShapeFileName); for a Shape file

      FeatureClassDefinition facilitySiteDefinition = enterpriseFeatureClass.GetDefinition();

      int ownTypeIndex = facilitySiteDefinition.FindField("OWNTYPE");
      int areaIndex = facilitySiteDefinition.FindField(facilitySiteDefinition.GetAreaField());

      EditOperation editOperation = new EditOperation();
      editOperation.Callback(context =>
      {
        QueryFilter queryFilter = new QueryFilter { WhereClause = "FCODE = 'Hazardous Materials Facility' AND OWNTYPE = 'Private'" };

        using (RowCursor rowCursor = enterpriseFeatureClass.Search(queryFilter, false))
        {
          while (rowCursor.MoveNext())
          {
            using (Feature feature = (Feature)rowCursor.Current)
            {
              // In order to update the Map and/or the attribute table.
              // Has to be called before any changes are made to the row
              context.Invalidate(feature);

              // Transfer all Hazardous Material Facilities to the City.
              feature[ownTypeIndex] = "Municipal";

              if (Convert.ToDouble(feature[areaIndex]) > 50000)
              {
                // Set the Shape of the feature to whatever you need.
                List<Coordinate2D> newCoordinates = new List<Coordinate2D>
                {
                  new Coordinate2D(1021570, 1880583),
                  new Coordinate2D(1028730, 1880994),
                  new Coordinate2D(1029718, 1875644),
                  new Coordinate2D(1021405, 1875397)
                };

                feature.SetShape(new PolygonBuilderEx(newCoordinates).ToGeometry());
              }

              feature.Store();

              // Has to be called after the store too
              context.Invalidate(feature);
            }
          }
        }
      }, enterpriseFeatureClass);

      try
      {
        modificationResult = editOperation.Execute();
        if (!modificationResult) message = editOperation.ErrorMessage;
      }
      catch (GeodatabaseException exObj)
      {
        message = exObj.Message;
      }
    }
  });

  if (!string.IsNullOrEmpty(message))
    MessageBox.Show(message);
}