library(raster)
dat = list()
dat$x = seq(1.5, by = 10, len = 10)
dat$y = seq(3.5, by = 10, len = 15)
dat$z = matrix(sample(c(0,1), size = 10*15, replace = T), 10, 15)

r=raster(dat);plot(r)

r_poly = rasterToPolygons(r, fun = function(r) {r == 1}, dissolve = F)
plot(r_poly, add = T)

b = extract(r,r_poly_new) # "r_poly_new" contains the combined polygons
str(b)                    # list of clearly separated polygons
tab = lapply(b,table)
tab

library(rgeos) ## For the function gArea

## Clump and polygonize
Rclus <- clump(r)
SPclus <- rasterToPolygons(Rclus, dissolve=TRUE)

## Check that this works
plot(SPclus, col = seq_along(SPclus))

## Get cluster areas from RasterLayer object
transform(data.frame(freq(Rclus)),
          area = count*prod(res(Rclus)))

## Get cluster areas from SpatialPolygons object
transform(data.frame(SPclus),
          area = gArea(SPclus, byid=TRUE))

## Using gArea as above is better than the following, which gives misleading
## results for projected data. (See ?"Polygons-class" for explanation)
## h.t. Robert Hijmans & Roger Bivand in the R-sig-geo thread starting here
## https://stat.ethz.ch/pipermail/r-sig-geo/2013-December/020065.html
transform(data.frame(SPclus),
         area = sapply(SPclus@polygons, function(X) X@area))

require(rgeos)
uni <- gUnion( r_poly , r_poly )
plot( uni , col = 2 )

m <- clump(r)
f <- freq(m)
f[,2] <- f[,2] * xres(r) * yres(r)

a <- area(r)
zonal(a, m, 'sum')