Public Shared Function Area( _
   ByVal polygon As Polygon, _
   Optional ByVal maxSegmentLength As Double _
) As Double

public static double Area( 
   Polygon polygon,
   double maxSegmentLength
)

<Grid x:Name="LayoutRoot">
    
  <!-- Define some Resources that can be used in other parts of the XAML file. -->
  <Grid.Resources>
    
    <!-- Define a SimpleFillSymbol to use as the initial display of the Polygon Graphic on the Map. -->
    <esri:SimpleFillSymbol x:Key="RedFillSymbol" BorderBrush="Black" BorderThickness="2" Fill="Red"/>
    
    <!-- Define a SimpleFillSymbol to use as the display of the Polygon Graphic on the Map after the user clicks the Button. -->
    <esri:SimpleFillSymbol x:Key="GreenFillSymbol" BorderBrush="Black" BorderThickness="2" Fill="Green"/>
    
    <!-- 
    Define a SpatialReference object that has the same WKID as the ArcGISTiledMapServiceLayer in
    the Map. This will allow for the Graphics in the GraphicsLayer to line up properly. 
    -->
    <esri:SpatialReference x:Key="theSpatialReference" WKID="4326"/>
    
  </Grid.Resources>
    
  <!-- Add a Map control with an ArcGISTiledMapServiceLayer. -->
  <esri:Map Background="White" HorizontalAlignment="Left" Margin="12,107,0,0" Name="Map1" 
          VerticalAlignment="Top" Height="318" Width="483"  WrapAround="True"
            Extent="-58.53,-38.95,69.42,45.28">
  
    <!--  Add a backdrop ArcGISTiledMapServiceLayer. The SpatialReference = 4326 (Geographic Coordinate System). -->
    <esri:ArcGISTiledMapServiceLayer ID="PhysicalTiledLayer" 
           Url="http://services.arcgisonline.com/ArcGIS/rest/services/ESRI_StreetMap_World_2D/MapServer"/>
  
    <!-- 
    Add a GraphicsLayer with a single Polygon. It is important to provide the GraphicsLayer with an 'ID' 
    Attribute so to be able to access it in the code-behind file. 
    -->
    <esri:GraphicsLayer ID="MyGraphicsLayer"  Initialized="GraphicsLayer_Initialized">
     
      <!--Add the Graphics to the GraphicsLayer. -->
      <esri:GraphicsLayer.Graphics>
        
        <!-- 
        Define a Polygon using the StaticResources for the Symbol and SpatialReference. The Geometry.Geodesic 
        Shared/static Methods that will be used when clicking the Button should work on Graphic features based 
        upon the Geographic Coordinate System (using Latitude/Longitude units).
        -->
        <esri:Graphic Symbol="{StaticResource RedFillSymbol}">
          <esri:Polygon SpatialReference="{StaticResource theSpatialReference}">
            <esri:Polygon.Rings>
              <esri:PointCollection>
                <esri:MapPoint X="15" Y="17" />
                <esri:MapPoint X="-18" Y="18" />
                <esri:MapPoint X="-40" Y="8" />
                <esri:MapPoint X="10" Y="-8" />
                <esri:MapPoint X="50" Y="5" />
                <esri:MapPoint X="15" Y="17" />
              </esri:PointCollection>
            </esri:Polygon.Rings>
          </esri:Polygon>
        </esri:Graphic>
  
      </esri:GraphicsLayer.Graphics>
     </esri:GraphicsLayer>
    
  </esri:Map>
  
  <!--Perform Geodesic.Areas calculations on the Polygon Graphic after it's Ring orientation has been corrected. -->
  <sdk:Label Height="17" HorizontalAlignment="Left" Margin="229,85,0,0" Name="Label_Areas" 
             VerticalAlignment="Top" Width="131" Content="Area (Square Meters): "/>
  <TextBox Height="23" HorizontalAlignment="Left" Margin="355,82,0,0" Name="TextBox_Areas" 
           VerticalAlignment="Top" Width="140" />
  <Button Content="Change ring verticies to clockwise" Height="23" HorizontalAlignment="Left" Margin="12,82,0,0" 
          Name="Button1" VerticalAlignment="Top" Width="198" Click="Button1_Click"/>
    
  <!-- Provide the instructions on how to use the sample code. -->
  <TextBlock Height="57" HorizontalAlignment="Left" Name="TextBlock1" VerticalAlignment="Top" Width="493" 
           TextWrapping="Wrap" Margin="2,9,0,0" 
           Text="Click the button to change the orientation of the vertices in the Ring of the Polygon from
             counter-clock-wise to clock-wise. Then the Geodesic.Area calculation will return a positive
             number." />
    
</Grid>

private void GraphicsLayer_Initialized(object sender, System.EventArgs e)
{
  // Once the GraphcsLayer has initialized call two different functions. One to perform the Geodesic.Area calculation
  // (via the DisplayArea function). The second to display the vertices of the Rings of the Polygon Graphic with a
  // TextSymbol so users can see the orientation of how the Polygon was constructed (via the 
  // DisplayPolygonVerticiesAsTextSymbol function). 
  DisplayArea();
  DisplayPolygonVerticesAsTextSymbol();
}
  
public void DisplayArea()
{
  // Get the GraphicsLayer that was defined in XAML. It contain a single Polygon Graphic.
  ESRI.ArcGIS.Client.GraphicsLayer theGraphicsLayer = (ESRI.ArcGIS.Client.GraphicsLayer)(Map1.Layers["MyGraphicsLayer"]);
  
  // Loop through the Graphics in the GraphicsLayer (there should only be one Polygon graphic).
  foreach (ESRI.ArcGIS.Client.Graphic theGraphic in theGraphicsLayer)
  {
    // Get the Geometry of the Graphic.
    ESRI.ArcGIS.Client.Geometry.Geometry theGeometry = theGraphic.Geometry;
    
    // Define a variable to hold the Geodesic.Area calculation.
    double theArea = 0;
    
    // Only process Polygon Graphics.
    if ((theGeometry) is ESRI.ArcGIS.Client.Geometry.Polygon)
    {
      // Cast the generic Geometry of the Graphic to a Polygon.
      ESRI.ArcGIS.Client.Geometry.Polygon thePolygon = (ESRI.ArcGIS.Client.Geometry.Polygon)theGeometry;
      
      // Calculate the Geodesic.Area of the Polygon.
      theArea = ESRI.ArcGIS.Client.Geometry.Geodesic.Area(thePolygon, 100);
    }
    
    // Display the Geodesic.Area to the user.
    TextBox_Areas.Text = theArea.ToString();
  }
}
  
private void Button1_Click(object sender, System.Windows.RoutedEventArgs e)
{
  // Define a new GeometryService that will re-orient the Rings of the Polygon Graphic to be clock-wise.
  ESRI.ArcGIS.Client.Tasks.GeometryService geometryService = new ESRI.ArcGIS.Client.Tasks.GeometryService("http://tasks.arcgisonline.com/ArcGIS/rest/services/Geometry/GeometryServer");
  
  // Add an EventHandler to process when the GeometryService is complete.
  geometryService.SimplifyCompleted += GeometryService_SimplifyCompleted;
  
  // Add an EvenHandler in case there is a problem with the GeometryService.
  geometryService.Failed += GeometryService_Failed;
  
  // Get the GraphicsLayer that was created in XAML with the Polygon Graphic.
  ESRI.ArcGIS.Client.GraphicsLayer theGraphicsLayer = (ESRI.ArcGIS.Client.GraphicsLayer)(Map1.Layers["MyGraphicsLayer"]);
  
  // Create a new List<Graphic> object. This is needed as an input for the GeometryService.SimplifyAsync Method.
  List<ESRI.ArcGIS.Client.Graphic> graphicList = new List<ESRI.ArcGIS.Client.Graphic>();
  
  // Loop through each Graphic in the GraphicsLayer.
  foreach (ESRI.ArcGIS.Client.Graphic theGraphic in theGraphicsLayer)
  {
    // If we have a Polygon Graphic do more processing.
    if ((theGraphic.Geometry) is ESRI.ArcGIS.Client.Geometry.Polygon)
    {
      // Add the Polygon Graphic into the GraphicList.
      graphicList.Add(theGraphic);
    }
  }
  
  // Call the Asynchronous GeometryService.SimplifyAsync Method.
  geometryService.SimplifyAsync(graphicList);
}
  
private void GeometryService_SimplifyCompleted(object sender, ESRI.ArcGIS.Client.Tasks.GraphicsEventArgs args)
{
  // The GeometryService.SimplifyAsync Method has completed! 
  
  // Get the GraphicsLayer defined in XAML. At this point there will be several Graphics because some additonal
  // MapPoint's were added using TextSymbols to show the order of vertices used to make up the Rings of the
  // Polygon Graphic.
  ESRI.ArcGIS.Client.GraphicsLayer theGraphicsLayer = (ESRI.ArcGIS.Client.GraphicsLayer)(Map1.Layers["MyGraphicsLayer"]);
  
  // Clear out all the Graphics in the GraphicsLayer.
  theGraphicsLayer.ClearGraphics();
  
  // Create a new Graphic that will hold the new Polygon with the Ring using the correct (i.e. clock-wise) vertex 
  // orientation which will give a positive Geodesic.Area calculation.
  ESRI.ArcGIS.Client.Graphic aGraphic = new ESRI.ArcGIS.Client.Graphic();
  
  // Get the new Polygon Graphic's Geometry from the return result of the GeometryService.SimplifyAsync Method.
  aGraphic.Geometry = args.Results[0].Geometry;
  
  // Set the Symbol of the new Polygon Graphic using one defined in XAML.
  aGraphic.Symbol = LayoutRoot.Resources["GreenFillSymbol"] as ESRI.ArcGIS.Client.Symbols.Symbol;
  
  // Add the new Polygon Graphic to the GraphicsLayer.
  theGraphicsLayer.Graphics.Add(aGraphic);
  
  // Call the same functions to re-render the map that was used when the application initially started. One to perform 
  // the Geodesic.Area calculation (via the DisplayArea function). The second to display the vertices of the Rings of 
  // the Polygon Graphic with a TextSymbol so users can see the orientation of how the Polygon was constructed (via the 
  // DisplayPolygonVerticiesAsTextSymbol function).
  DisplayArea();
  DisplayPolygonVerticesAsTextSymbol();
}
  
private void GeometryService_Failed(object sender, ESRI.ArcGIS.Client.Tasks.TaskFailedEventArgs e)
{
  // We have a problem with the GeometryService.SimplifyAsync Method. Display the issue to the user.
  MessageBox.Show("Geometry Service error: " + e.Error.Message);
}
  
public void DisplayPolygonVerticesAsTextSymbol()
{
  // This function will show the order of the vertices for the Rings of the Polygon Graphic. This will help the 
  // user see visually whether the Rings are clock-wise (which yield a positive Geodesic.Area calculation) or
  // counter-clock-wise (which yield a negative Geodesic.Area calculation).
  
  // Get the GraphicsLayer that was defined in XAML.
  ESRI.ArcGIS.Client.GraphicsLayer theGraphicsLayer = (ESRI.ArcGIS.Client.GraphicsLayer)(Map1.Layers["MyGraphicsLayer"]);
  
  // Create a temporary Polygon that will be used to obtain the vertices in the Rings.
  ESRI.ArcGIS.Client.Geometry.Polygon theTemporaryPolygon = null;
  
  // Loop through all of the Graphics in the GraphicsLayer (we should just have one Polygon Graphic at this point).
  foreach (ESRI.ArcGIS.Client.Graphic theGraphic in theGraphicsLayer)
  {
    // Get the Geometry of the Graphic.
    ESRI.ArcGIS.Client.Geometry.Geometry theGeometry = theGraphic.Geometry;
    
    // Only process Polygon Graphics.
    if ((theGeometry) is ESRI.ArcGIS.Client.Geometry.Polygon)
    {
      // Set the temporay Polygon to be the Geometry of the Polygon in the GraphicsLayer.
      theTemporaryPolygon = (ESRI.ArcGIS.Client.Geometry.Polygon)theGeometry;
    }
  }
  
  // Get the ObservableCollection<PointCollecton> from the temporary Polygon. This has the Ring of vertices. 
  System.Collections.ObjectModel.ObservableCollection<ESRI.ArcGIS.Client.Geometry.PointCollection> theObservableCollectionOfPointCollection = theTemporaryPolygon.Rings;
  
  // Loop through each PointCollection in the ObservableCollection<PointCollecton>.
  foreach (ESRI.ArcGIS.Client.Geometry.PointCollection myPointCollection in theObservableCollectionOfPointCollection)
  {
    // Loop through all of the vertices in the Ring that defines the Polygon. Note: Don't process the last
    // vertex (i.e. myPointCollection.Count - 1) since the first and last vertex are the same in the Ring.
    for (int x = 0; x <= myPointCollection.Count - 2; x++)
    {
      // Create a new TextSymbol and define its look. The strings used to define the FontFamily can be
      // found in the following MSDN documentation:
      // http://msdn.microsoft.com/en-us/library/cc189010(v=VS.95).aspx
      ESRI.ArcGIS.Client.Symbols.TextSymbol aTextSymbol = new ESRI.ArcGIS.Client.Symbols.TextSymbol();
      aTextSymbol.FontFamily = new FontFamily("Arial");
      aTextSymbol.FontSize = 20;
      aTextSymbol.Foreground = new System.Windows.Media.SolidColorBrush(Colors.Black);
      
      // Set the TextSymbol.Text Property to the index order of the vertices in the Ring.
      aTextSymbol.Text = x.ToString();
      
      // Assign the TextSymbol as the Graphic.Symbol as this was not previously done.
      ESRI.ArcGIS.Client.Graphic myVertexGraphic = new ESRI.ArcGIS.Client.Graphic();
      myVertexGraphic.Geometry = myPointCollection[x];
      myVertexGraphic.Symbol = (ESRI.ArcGIS.Client.Symbols.Symbol)aTextSymbol;
      
      // Add the MapPoints that display the vertex order to the GraphicsLayer.
      theGraphicsLayer.Graphics.Add(myVertexGraphic);
    }
  }
}

Private Sub GraphicsLayer_Initialized(sender As System.Object, e As System.EventArgs)
  
  ' Once the GraphcsLayer has initialized call two different functions. One to perform the Geodesic.Area calculation
  ' (via the DisplayArea function). The second to display the vertices of the Rings of the Polygon Graphic with a
  ' TextSymbol so users can see the orientation of how the Polygon was constructed (via the 
  ' DisplayPolygonVerticiesAsTextSymbol function). 
  DisplayArea()
  DisplayPolygonVerticesAsTextSymbol()
  
End Sub
  
Public Sub DisplayArea()
  
  ' Get the GraphicsLayer that was defined in XAML. It contain a single Polygon Graphic.
  Dim theGraphicsLayer As ESRI.ArcGIS.Client.GraphicsLayer = CType(Map1.Layers("MyGraphicsLayer"), ESRI.ArcGIS.Client.GraphicsLayer)
    
  ' Loop through the Graphics in the GraphicsLayer (there should only be one Polygon graphic).
  For Each theGraphic As ESRI.ArcGIS.Client.Graphic In theGraphicsLayer
    
    ' Get the Geometry of the Graphic.
    Dim theGeometry As ESRI.ArcGIS.Client.Geometry.Geometry = theGraphic.Geometry
    
    ' Define a variable to hold the Geodesic.Area calculation.
    Dim theArea As Double = Nothing
     
    ' Only process Polygon Graphics.
    If TypeOf (theGeometry) Is ESRI.ArcGIS.Client.Geometry.Polygon Then
        
      ' Cast the generic Geometry of the Graphic to a Polygon.
      Dim thePolygon As ESRI.ArcGIS.Client.Geometry.Polygon = CType(theGeometry, ESRI.ArcGIS.Client.Geometry.Polygon)
       
      ' Calculate the Geodesic.Area of the Polygon.
      theArea = ESRI.ArcGIS.Client.Geometry.Geodesic.Area(thePolygon, 100)
    End If
    
    ' Display the Geodesic.Area to the user.
    TextBox_Areas.Text = theArea.ToString
    
  Next
  
End Sub
            
Private Sub Button1_Click(sender As System.Object, e As System.Windows.RoutedEventArgs)
    
  ' Define a new GeometryService that will re-orient the Rings of the Polygon Graphic to be clock-wise.
  Dim geometryService As New ESRI.ArcGIS.Client.Tasks.GeometryService("http://tasks.arcgisonline.com/ArcGIS/rest/services/Geometry/GeometryServer")
  
  ' Add an EventHandler to process when the GeometryService is complete.
  AddHandler geometryService.SimplifyCompleted, AddressOf GeometryService_SimplifyCompleted
    
  ' Add an EvenHandler in case there is a problem with the GeometryService.
  AddHandler geometryService.Failed, AddressOf GeometryService_Failed
  
  ' Get the GraphicsLayer that was created in XAML with the Polygon Graphic.
  Dim theGraphicsLayer As ESRI.ArcGIS.Client.GraphicsLayer = CType(Map1.Layers("MyGraphicsLayer"), ESRI.ArcGIS.Client.GraphicsLayer)
    
  ' Create a new List(Of Graphic) object. This is needed as an input for the GeometryService.SimplifyAsync Method.
  Dim graphicList As New List(Of ESRI.ArcGIS.Client.Graphic)()
  
  ' Loop through each Graphic in the GraphicsLayer.
  For Each theGraphic As ESRI.ArcGIS.Client.Graphic In theGraphicsLayer
    
    ' If we have a Polygon Graphic do more processing.
    If TypeOf (theGraphic.Geometry) Is ESRI.ArcGIS.Client.Geometry.Polygon Then
      
      ' Add the Polygon Graphic into the GraphicList.
      graphicList.Add(theGraphic)
      
    End If
    
  Next
  
  ' Call the Asynchronous GeometryService.SimplifyAsync Method.
  geometryService.SimplifyAsync(graphicList)
  
End Sub
            
Private Sub GeometryService_SimplifyCompleted(ByVal sender As Object, ByVal args As ESRI.ArcGIS.Client.Tasks.GraphicsEventArgs)
  
  ' The GeometryService.SimplifyAsync Method has completed! 
  
  ' Get the GraphicsLayer defined in XAML. At this point there will be several Graphics because some additonal
  ' MapPoint's were added using TextSymbols to show the order of vertices used to make up the Rings of the
  ' Polygon Graphic.
  Dim theGraphicsLayer As ESRI.ArcGIS.Client.GraphicsLayer = CType(Map1.Layers("MyGraphicsLayer"), ESRI.ArcGIS.Client.GraphicsLayer)
  
  ' Clear out all the Graphics in the GraphicsLayer.
  theGraphicsLayer.ClearGraphics()
  
  ' Create a new Graphic that will hold the new Polygon with the Ring using the correct (i.e. clock-wise) vertex 
  ' orientation which will give a positive Geodesic.Area calculation.
  Dim aGraphic As New ESRI.ArcGIS.Client.Graphic
  
  ' Get the new Polygon Graphic's Geometry from the return result of the GeometryService.SimplifyAsync Method.
  aGraphic.Geometry = args.Results(0).Geometry
   
  ' Set the Symbol of the new Polygon Graphic using one defined in XAML.
  aGraphic.Symbol = TryCast(LayoutRoot.Resources("GreenFillSymbol"), ESRI.ArcGIS.Client.Symbols.Symbol)
   
  ' Add the new Polygon Graphic to the GraphicsLayer.
  theGraphicsLayer.Graphics.Add(aGraphic)
  
  ' Call the same functions to re-render the map that was used when the application initially started. One to perform 
  ' the Geodesic.Area calculation (via the DisplayArea function). The second to display the vertices of the Rings of 
  ' the Polygon Graphic with a TextSymbol so users can see the orientation of how the Polygon was constructed (via the 
  ' DisplayPolygonVerticiesAsTextSymbol function).
  DisplayArea()
  DisplayPolygonVerticesAsTextSymbol()
  
End Sub
 
Private Sub GeometryService_Failed(ByVal sender As Object, ByVal e As ESRI.ArcGIS.Client.Tasks.TaskFailedEventArgs)
  
  ' We have a problem with the GeometryService.SimplifyAsync Method. Display the issue to the user.
  MessageBox.Show("Geometry Service error: " + e.Error.Message)
  
End Sub
            
Public Sub DisplayPolygonVerticesAsTextSymbol()
  
  ' This function will show the order of the vertices for the Rings of the Polygon Graphic. This will help the 
  ' user see visually whether the Rings are clock-wise (which yield a positive Geodesic.Area calculation) or
  ' counter-clock-wise (which yield a negative Geodesic.Area calculation).
  
  ' Get the GraphicsLayer that was defined in XAML.
  Dim theGraphicsLayer As ESRI.ArcGIS.Client.GraphicsLayer = CType(Map1.Layers("MyGraphicsLayer"), ESRI.ArcGIS.Client.GraphicsLayer)
  
  ' Create a temporary Polygon that will be used to obtain the vertices in the Rings.
  Dim theTemporaryPolygon As ESRI.ArcGIS.Client.Geometry.Polygon = Nothing
  
  ' Loop through all of the Graphics in the GraphicsLayer (we should just have one Polygon Graphic at this point).
  For Each theGraphic As ESRI.ArcGIS.Client.Graphic In theGraphicsLayer
    
    ' Get the Geometry of the Graphic.
    Dim theGeometry As ESRI.ArcGIS.Client.Geometry.Geometry = theGraphic.Geometry
     
    ' Only process Polygon Graphics.
    If TypeOf (theGeometry) Is ESRI.ArcGIS.Client.Geometry.Polygon Then
      
      ' Set the temporay Polygon to be the Geometry of the Polygon in the GraphicsLayer.
      theTemporaryPolygon = CType(theGeometry, ESRI.ArcGIS.Client.Geometry.Polygon)
    End If
    
  Next
  
  ' Get the ObservableCollection(OfPointCollecton) from the temporary Polygon. This has the Ring of vertices. 
  Dim theObservableCollectionOfPointCollection As Collections.ObjectModel.ObservableCollection(Of ESRI.ArcGIS.Client.Geometry.PointCollection) = theTemporaryPolygon.Rings
  
  ' Loop through each PointCollection in the ObservableCollection(OfPointCollecton).
  For Each myPointCollection As ESRI.ArcGIS.Client.Geometry.PointCollection In theObservableCollectionOfPointCollection
    
    ' Loop through all of the vertices in the Ring that defines the Polygon. Note: Don't process the last
    ' vertex (i.e. myPointCollection.Count - 1) since the first and last vertex are the same in the Ring.
    For x As Integer = 0 To myPointCollection.Count - 2
      
      ' Create a new TextSymbol and define its look. The strings used to define the FontFamily can be
      ' found in the following MSDN documentation:
      ' http://msdn.microsoft.com/en-us/library/cc189010(v=VS.95).aspx
      Dim aTextSymbol As New ESRI.ArcGIS.Client.Symbols.TextSymbol
      aTextSymbol.FontFamily = New FontFamily("Arial")
      aTextSymbol.FontSize = 20
      aTextSymbol.Foreground = New System.Windows.Media.SolidColorBrush(Colors.Black)
      
      ' Set the TextSymbol.Text Property to the index order of the vertices in the Ring.
      aTextSymbol.Text = x.ToString
      
      ' Assign the TextSymbol as the Graphic.Symbol as this was not previously done.
      Dim myVertexGraphic As New ESRI.ArcGIS.Client.Graphic
      myVertexGraphic.Geometry = myPointCollection.Item(x)
      myVertexGraphic.Symbol = CType(aTextSymbol, ESRI.ArcGIS.Client.Symbols.Symbol)
      
      ' Add the MapPoints that display the vertex order to the GraphicsLayer.
      theGraphicsLayer.Graphics.Add(myVertexGraphic)
    Next
    
  Next
  
End Sub