R GIS: Terrain Analysis for Polygons as Simple as it Gets!

library(rgdal)
library(raster)

alt <- getData('alt', country = "AT")
gadm <- getData('GADM', country = "AT", level = 2)
gadm_sub <- gadm[sample(1:length(gadm), 5), ]

plot(alt)
plot(gadm_sub, add=T)

asp <- terrain(alt, opt = "aspect", unit = "degrees", df = F)
slo <- terrain(alt, opt = "slope", unit = "degrees", df = F)

> extract(slo, gadm_sub, fun = mean, na.rm = T, small = T, df = T)
  ID     slope
1  1  9.959053
2  2  1.047443
3  3  7.456165
4  4  1.673786
5  5 11.946553

> extract(asp, gadm_sub, fun = mean, na.rm = T, small = T, df = T)
  ID   aspect
1  1 170.8065
2  2 184.0130
3  3 190.7155
4  4 136.8953
5  5 205.2115