I am not sure what you meant by "extent". Did you mean the actual shape area or the "envelope" of the polygon, or else?
If each of your shapefiles contains only one polygon, here is a way to combine them and get an average shape area value:
1. Run the Merge tool (Data Management toolbox - General toolset) to combine all shapefiles into one.
2. Use the Add Field tool to add a double field.
3. Use the Calculate Field tool with the Python expression !shape.area! to get area values for the new field. You now have the area value for each polygon.
4. Run Summary Statistics tool to get the average value from the new field.
You mentioned "visualize". I guess you want to derive a representative shape from all the polygons. That needs some work. If the polygon shapes are very similar, you can try this workaround:
1. Once the polygons are Merged into one file, run Feature To Line tool (Data Management toolbox - Features toolset, requiring ArcInfo license) to get the boundaries as polylines.
2. Run the Buffer tool with a distance that can result in a ring-like polygon containing most of the polylines without small holes. There is a new tool in ArcGIS 10, Eliminate Polygon Part (ArcInfo License), that can remove holes.
3. Run the Feature To Raster tool (Conversion toolbox - To Raster toolset) to convert the buffer polygon into a raster.
4. Run the Thin tool (Spatial Analyst toolbox - Generalization toolset) to reduce the buffer polygon to a raster "line", like a centerline.
5. Run the Raster To Polyline tool (Conversion toolbox - From Raster toolset) to convert the thin raster to a (closed) polyline.
5. Run the Feature To Polygon tool (Data Management toolbox - Features toolset, requiring ArcInfo license) to get a polygon from the closed polyline. This could be a "representative" shape for all your polygons.
Hope this gives you some leads.
