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);
}