These functions use the Chamberlain-Duquette formula, which is suitable for geographic coordinates on a sphere. They return area in square meters.
Examples
fp <- system.file("shape/nc.shp", package = "sf")
nc <- as.data.frame(read_shapefile(fp))
# square meters, not square degrees
head(as.vector(ga_unsigned_area_cd(nc$geometry)))
#> [1] 1139433024 611704011 1426267143 695828090 1523251541 969518599
head(as.vector(ga_signed_area_cd(nc$geometry)))
#> [1] -1139433024 -611704011 -1426267143 -695828090 -1523251541 -969518599