@akasasbt You stated "From your output, the area of the whole region is 3080.9986 (half of this is 1540.4993) and the area above centroid is 1514.0829, where there is a 1.7% difference in area."
Note, a centroid does not necessarily define a cutting plane where half the area is on either side. It is a measure of how an area is distributed. Consider a "T" shaped area.