Area of segment in a given slice?

This should do what you need (this script puts results in a table but you can easily create a plot from the vtkDoubleArray):

segmentationNode = getNode('Segmentation')
segmentId = 'Segment_1'

# Get segment as a numpy array
import vtk.util.numpy_support
import numpy as np
vimage = segmentationNode.GetBinaryLabelmapRepresentation(segmentId)
narray = vtk.util.numpy_support.vtk_to_numpy(vimage.GetPointData().GetScalars())
vshape = vimage.GetDimensions()

# Reshape the segment volume to have an array of slices
narrayBySlice = narray.reshape([-1,vshape[1]*vshape[2]])

# Count number of >0 voxels for each slice
narrayBySlicePositive = narrayBySlice[:]>0
areaBySliceInVoxels = np.count_nonzero(narrayBySlicePositive, axis=1)

# Convert number of voxels to area in mm2
areaOfPixelMm2 = vimage.GetSpacing()[0] * vimage.GetSpacing()[1]
areaBySliceInMm2 = areaBySliceInVoxels * areaOfPixelMm2

# Save results to a new table node
tableNode=slicer.mrmlScene.AddNewNodeByClass("vtkMRMLTableNode", "Segment quantification")
updateTableFromArray(tableNode, areaBySliceInMm2)
tableNode.GetTable().GetColumn(0).SetName("Segment Area")