Irregular Polygons and Differences in Area

[Anonymous User]

I have a polygon FC that has been divided in 4 zones and that is further divided into subzones and exported as a new FC. 

The issue is that the area of the original polygon (encompasses the entire city limits) has a larger area than the sum of all the sub zones put together.

For the sake of testing, I created two new fields called AREA in the original FC and the subdivided FC; both FC are in the same coordinate system and when calculating the geometry using the GP Tool I did not select a Coordinate system.

Is there a mathematical explanation concerning irregular polygons, their shape and why when combined their area would not equal the original polygon that they were split from?

AREA:

AREA: 

[DanPatterson]

It is hard to tell from the figure, are there 9 or 10 areas after the split? (see the very middle of the figure)

And was the last entry in the table the total?

[Anonymous User]

10 after split 

and no the second table is not totaled, they are the areas for the 10 new polygons

[Anonymous User]

I went through an additional workflow where I merged the 10 sub-zones together, clipped them to the city limits (original fc) and then ran the SYMMETRICAL DIFFERENCE.

After running the SYMMETRICAL DIFFERENCE I RESHAPED by snapping to and TRACING along the city limits.

Once the symmetrical differences were taken care of, the was a difference of less than 1sq.ft. 

Finally to check my work I performed to additional steps by performing a SPATIAL JOINE and Copy Paste Special with FC with 10 polygons to the the MERGED polygon made up of the 10 sub-zones, which concluded in giving me the relatively same difference.

[Anonymous User]

The same difference that I started with in the original post.***

[Anonymous User]

The spatial join and copy paste special were independent of each other, the were ran as two different process to have two outputs to compare to the original difference.***

[DanPatterson]

Did you run a check geometry on the file?  Or run a FeatureClassToFeatureClass to get a copy (it runs a repair during the process)

The differences are indeed significant and I am wondering if there is a part underneath another part.  The only way to check for that is to select each shape on the map one at a time and check what the outline looks like relative to what is expected

[Anonymous User]

I ran check Geometry and it output zero records and running the FeatureClasstoFeatureClass produced the same areas and difference. 

Going through I did find some gaps between the zones, but when I RESHAPED the polygons, the difference was greater after doing so. After filling the gaps the difference was over 15000 sq.ft.

[DanPatterson]

out of ideas other than start again with a clean slate