Introducing Geographic Information Systems with ArcGIS: A Workbook Approach to Learning GIS, 3rd Edition

Polygons within Polygons—Perimeter and Area Calculations

In representing the natural environment or the human-built world, we frequently want to employ plane areas that are included in other plane areas: lakes in a county, for example; islands in a lake; wetlands that are internal to an island; and so on. As mentioned, many polygons are disjoint (that is, if you look at the area covered by a polygon, you see no other polygons), but others are nested (when you look at a polygon you see other polygons within it). The areas of all ArcGIS polygons are mutually exclusive. Each has an identification, an area measurement, and a perimeter measurement. Each has its own set of attribute values. Geographically, however, they may be arranged in two different ways. Consider Figure 4-7 with feature class representations A and B. The small squares are 1 unit on a side.

FIGURE 4-7 A nested polygon compared with an adjacent polygon

Feature class A consists of two lines and two polygons (P and Q). Polygon Q is a nested polygon with respect to polygon P.

Feature class B consists of three lines and two polygons (R and S). Polygon S is not a nested polygon. It is simply an area disjoint from polygon R.

The area of polygon P is 8 square units, calculated as ((3*3) – (1*1)); that is also the area of polygon R. The area of polygon Q is 1 square unit; that is also the area of polygon S.

The perimeter ...