Trying to find area using SHAPE#AREA - cursor

Question

I am trying to get the area of each polygon in the .shp file and then append it to a new column in the attribute table.
import os
import arcpy
import math
folderpath = 'C:\Users\Michaelf\Desktop\GEOG M173'
arcpy.env.workspace = folderpath
arcpy.env.overwriteOutput = True
input_shp = folderpath + r'\lower48_county_2012_election.shp'
equal_shape = folderpath + r'\project_lower48.shp'
out_point = folderpath + r'\lower_48_centroid.shp'
out_shp = folderpath + r'\48_State_Centroids.shp'
totarea = []
arcpy.AddField_management(input_shp, "totarea")
geometryField = arcpy.Describe(totarea).shapeFieldName
cursor = arcpy.UpdateCursor(totarea)
for row in cursor:
AreaValue = row.getValue(geometryField).area
row.setValue("total_area",AreaValue)
cursor.updateRow(row)
del row, cursor
print AreaValue
Below is one suggestion I've received but I don't quite understand it
with arcpy.da.SearchCursor(input_shp, ("OID#", "SHAPE#AREA")) as cursor:
for row in cursor:
print("Feature {0} has an area of {1}".format(row[0], row[1]))
Here is my error message:
Traceback (most recent call last):
File "C:/Users/Michaelf/Desktop/GEOG M173/test2.py", line 16, in <module>
geometryField = arcpy.Describe(totarea).shapeFieldName
File "C:\Program Files (x86)\ArcGIS\Desktop10.3\ArcPy\arcpy\__init__.py", line 1246, in Describe
return gp.describe(value)
File "C:\Program Files (x86)\ArcGIS\Desktop10.3\ArcPy\arcpy\geoprocessing\_base.py", line 374, in describe
self._gp.Describe(*gp_fixargs(args, True)))
RuntimeError: Object: Describe input value is not valid type

Answer 1

Since it's a geometry-centric database, Arc automatically stores the total area of a polygon as an attribute. There's no need to calculate it, which is why (I assume) that code snippet was suggested to you:
with arcpy.da.SearchCursor(input_shp, ("OID#", "SHAPE#AREA")) as cursor:
for row in cursor:
print("Feature {0} has an area of {1}".format(row[0], row[1]))
This does the following:
Create a cursor to go through the input shapefile input_shp, pulling just two attributes (the object ID and the total area).
Loop through the shapefile one row at a time.
For each row, print out row[0] (the object ID) and row[1] (the total area).
For further reading I'd take a look at this excellent answer on GIS.SE. It explores some of the options for accessing and calculating geometry in detail.
(Final note: the shape#area attribute will be in the units of the data's projection. Be aware of this if you're getting unexpected numbers.)