Create square polygons from single centre coordinates and area in R - r

Question

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.

Answer 1

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")

Answer 2

Just to update this a bit, here is an sf solution.
Function to create the square buffers
bSquare <- function(x, a) {
a <- sqrt(a)/2
return( sf::st_buffer(x, dist = a, nQuadSegs=1,
endCapStyle = "SQUARE") )
}
Some example data
library(sf)
xy <- st_as_sf(data.frame(x = c(1,3,6,7),
y = c(3,2,7,8), z = c(38,23,12,12),
area = c(32,23,45,67)),
coords = c("x", "y"),
agr = "constant")
With variable buffer
sb.var <- bSquare(xy, xy$area)
plot(st_geometry(sb.var))
plot(st_geometry(xy), pch=20, add=TRUE)
With fixed buffer
sb <- bSquare(xy, 32)
plot(st_geometry(sb))
plot(st_geometry(xy), pch=20, add=TRUE)