Create square polygons from single centre coordinates and area in R

I am having issues plotting true to geographic extent pixels in R. the files come with a list of daily single coordinates and pixel size (area). There is also a Z element separate from this. The data structure looks this way:

 X <- c(1,3,6,7)
 Y <- c(3,2,7,8)
 Z <- c(38,23,12,12)
 Area <- c(32,23,45,67)

The X and Y are in degrees longitude and latitude while the area is in square kilometres. I create the point features easily using:

library(sp)
A <- cbind(X,Y,Z,Area)
B <- SpatialPoints(A)

I plot these easily using the area values to determine the "cex" for plotting. The Z column is intensity and I use these values to determine the colours . How do I create spatial polygons features using the areas for each point in R? I would be using these points to create gridded rasters.

This should do the trick:

library(rgeos)      ## for gBuffer()
library(raster)     ## for bind()

ww <- sqrt(B$Area)/2  ## Widths of buffers needed to produce desired areas    

pp <- list()
for(i in seq_along(B)) {
    pp[i] <- gBuffer(B[i], width=ww[i], quadsegs=1, capStyle="SQUARE")
}
PP <- do.call(bind, pp)

## Check that it worked
plot(PP)
plot(B, add=TRUE)
text(B, labels=1:4, adj=c(-1,0), col="red")