Public Overloads Shared Function Length( _
   ByVal polygon As Polygon _
) As Double

public static double Length( 
   Polygon polygon
)

<Grid x:Name="LayoutRoot">
            
  <!-- Add a Map control. -->
  <esri:Map Background="White" HorizontalAlignment="Left" Margin="12,107,0,0" Name="Map1" 
          VerticalAlignment="Top" Height="318" Width="483"  WrapAround="True"
            Extent="-22198191,5927190,-11909781,12700926">
      
    <!-- Add a background ArcGISTiledImageServiceLayer. -->
    <esri:ArcGISTiledMapServiceLayer ID="BaseMap" 
                 Url="http://services.arcgisonline.com/ArcGIS/rest/services/Canvas/World_Light_Gray_Base/MapServer" />
            
    <!-- 
    Add a FeatureLayer of the United States polygons. Set a Where clause to only return the state of Alaska. The 
    SpatialReference.WKID = 102100 (3857) which is a Projected Coordinate System. This means that in order to calculate 
    the perimeter Length accurately using the Geodesic.Length Shared/static Method, it is required to first convert the
    Polygon Geometry of Alaska into SpatialReference.WKID = 4326 in the Geographic Coordinate System.
    -->
    <esri:FeatureLayer ID="USStates" Where="ST_ABBREV = 'AK'" OutFields="*"
          Url="http://services.arcgisonline.com/ArcGIS/rest/services/Demographics/USA_1990-2000_Population_Change/MapServer/4"/>
    
  </esri:Map>
  
  <!-- Add a button to calculate the Geodesic.Length-->
  <sdk:Label Height="17" HorizontalAlignment="Left" Margin="258,82,0,0" Name="Label_Length" 
             VerticalAlignment="Top" Width="99" Content="Length (meters): "/>
  <TextBox Height="23" HorizontalAlignment="Left" Margin="355,82,0,0" Name="TextBox_Length" 
           VerticalAlignment="Top" Width="140" />
  <Button Content="Get the Geodesic.Length" Height="23" HorizontalAlignment="Left" Margin="12,82,0,0" 
          Name="Button1" VerticalAlignment="Top" Width="222" Click="Button1_Click"/>
  
  <!-- Provide the instructions on how to use the sample code. -->
  <TextBlock Height="67" HorizontalAlignment="Left" Name="TextBlock1" VerticalAlignment="Top" Width="670" 
           TextWrapping="Wrap" Margin="2,9,0,0" 
           Text="Click on the Button to calcuate the Geodesic.Length of the perimiter of the state of Alaska.
           The FeatureLayer that has the Polygon geometries are in the SpatialReference.WKID = 102100 (3857) 
           which is a Projected Coordinate System. This means that in order to calculate the perimeter Length 
           accurately using the Geodesic.Length Shared/static Method, it is required to first convert the 
           Polygon Geometry of Alaska into SpatialReference.WKID = 4326 in the Geographic Coordinate System." />
            
</Grid>

private void Button1_Click(object sender, System.Windows.RoutedEventArgs e)
{
  // Get the FeatureLayer that was defined in XAML. All of the features in the FeatureLayer are based upon
  // the SpatialReference.WKID = 102100 (3857) Projected Coordinate System.
  ESRI.ArcGIS.Client.FeatureLayer theFeatureLayer = (ESRI.ArcGIS.Client.FeatureLayer)(Map1.Layers["USStates"]);
  
  // Get the GraphicCollection from the FeatureLayer.
  ESRI.ArcGIS.Client.GraphicCollection theGraphicCollection = theFeatureLayer.Graphics;
  
  // Loop through all of the Graphics. We should only have one, Alaksa, since there was a restrictive
  // Where clause placed on the FeatureLayer defined in XAML.
  foreach (ESRI.ArcGIS.Client.Graphic aGraphic in theGraphicCollection)
  {
    // Get the Geometry of the Graphic. 
    ESRI.ArcGIS.Client.Geometry.Geometry theGeometry = aGraphic.Geometry;
    
    // Define a new WebMercator utility object.
    ESRI.ArcGIS.Client.Projection.WebMercator myWebMercator = new ESRI.ArcGIS.Client.Projection.WebMercator();
    
    // Define a new Geometry object that will have the SpatialReference.WKID = 4326 Geographic Coordinate System. 
    // The new Geometry object is obtained using the WebMercator.ToGeographic utility helper Method.
    ESRI.ArcGIS.Client.Geometry.Geometry WGS84GeographicGeometry = myWebMercator.ToGeographic(theGeometry);
    
    // Only process Polygon type of geometries.
    if (WGS84GeographicGeometry is ESRI.ArcGIS.Client.Geometry.Polygon)
    {
      // Cast the generic Geometry to the specific Polygon type.
      ESRI.ArcGIS.Client.Geometry.Polygon thePolygon = (ESRI.ArcGIS.Client.Geometry.Polygon)WGS84GeographicGeometry;
      
      // Obtain the Geodesic.Length from the Polygon.
      double theLength = ESRI.ArcGIS.Client.Geometry.Geodesic.Length(thePolygon);
     
      // Display the results to the user.
      TextBox_Length.Text = theLength.ToString();
    }
  }
}

Private Sub Button1_Click(sender As System.Object, e As System.Windows.RoutedEventArgs)
  
  ' Get the FeatureLayer that was defined in XAML. All of the features in the FeatureLayer are based upon
  ' the SpatialReference.WKID = 102100 (3857) Projected Coordinate System.
  Dim theFeatureLayer As ESRI.ArcGIS.Client.FeatureLayer = CType(Map1.Layers("USStates"), ESRI.ArcGIS.Client.FeatureLayer)
  
  ' Get the GraphicCollection from the FeatureLayer.
  Dim theGraphicCollection As ESRI.ArcGIS.Client.GraphicCollection = theFeatureLayer.Graphics
  
  ' Loop through all of the Graphics. We should only have one, Alaksa, since there was a restrictive
  ' Where clause placed on the FeatureLayer defined in XAML.
  For Each aGraphic As ESRI.ArcGIS.Client.Graphic In theGraphicCollection
    
    ' Get the Geometry of the Graphic. 
    Dim theGeometry As ESRI.ArcGIS.Client.Geometry.Geometry = aGraphic.Geometry
    
    ' Define a new WebMercator utility object.
    Dim myWebMercator As New ESRI.ArcGIS.Client.Projection.WebMercator
    
    ' Define a new Geometry object that will have the SpatialReference.WKID = 4326 Geographic Coordinate System. 
    ' The new Geometry object is obtained using the WebMercator.ToGeographic utility helper Method.
    Dim WGS84GeographicGeometry As ESRI.ArcGIS.Client.Geometry.Geometry = myWebMercator.ToGeographic(theGeometry)
    
    ' Only process Polygon type of geometries.
    If TypeOf WGS84GeographicGeometry Is ESRI.ArcGIS.Client.Geometry.Polygon Then
      
      ' Cast the generic Geometry to the specific Polygon type.
      Dim thePolygon As ESRI.ArcGIS.Client.Geometry.Polygon = CType(WGS84GeographicGeometry, ESRI.ArcGIS.Client.Geometry.Polygon)
      
      ' Obtain the Geodesic.Length from the Polygon.
      Dim theLength As Double = ESRI.ArcGIS.Client.Geometry.Geodesic.Length(thePolygon)
      
      ' Display the results to the user.
      TextBox_Length.Text = theLength.ToString
      
    End If
    
  Next
  
End Sub