Hi, I'm not sure I understand your question, but try this: - convert your polygon feature class to a raster using Feature to Raster - Use this raster as a zone raster in the Zonal Statistics tool, with "MEAN" as statistics type.
If its the boundary and not the area (entire polygon) you are after then use the Feature to Line tool to convert your polygon to a polyline then use the Polyline to Raster tool (make sure snap raster environment is set to your raster) to convert the line to a raster representation of your polyline and then you can use the Zonal Statistics tool.
