Equal area projections with different area results in ArcGIS for Desktop?

Question

Using ArcGIS, I have to calculate areas of huge polygons all over the Pacific Oceans betwwen 20N and 30S. I have been trying different Equal-areas projections (Cylindrical and sinusoidal for example) and found different results for the area claculation.

For example, one polygon is having a surface of 1'604'176 km2 with Cylindrical and a surface of 1'605'483 km2 with sinusoidal...

So my questions are:

Am i correct to use Equal area projections for calculating areas? Should i be using a different type of projections (equidistance...)?

How can you have different results between the projections and which one should be consider best?

At last, using an equal area projection, I discover that if I break down a big polygon into 6 smaller polygons and i compare the sum of the areas of the 6 smaller polygons with the area of the big polygon, i have a difference between the values (difference of 60Km2 for a polygon of 1'600'000Km2). How is it possible?

Answer 1

It is correct to use an equal area projection in order to compute the area of your polygon.

However, in your case, you should be aware that only the vertices of a polygon are projected when you change the coordinate system. Between the vertices, straight lines are then interpolated (but if you have a huge polygons, those lines should have been curves), which could explain why your areas are not exactly the same.

In order to avoid this problem, one workaround is to densify your polygon before you project it. The projection will then be more precise. As mentioned by @whuber, the densification of the polygon should be done in the original coordinate system (the one used when the polygon was digitized) in order to achieve an accurate result.

As a remark, this is also what occurs when you cut your polygon in pieces: cutting will add new vertices.