I'm trying to determine the area of occurence from a large polygon superimposed onto 2km x 2km grids. The goal is to have a slightly coarser answer then a straight area of the original polygon as the final area calculated will be the sum of all the grids that touch the polygon multiplied by 4 square km.
I tried to do this by creating a vector grid of 2000m x 2000m and then clipped the vector grid with the original polygon to get a total number of grids. I then multiplied it by 4. But the issue I'm having is that the area of the grids is smaller then the original. This shouldn't be as all the small slivers of the grids on the exterior of the shape should be counted as full size.
Then I have 251889 attributes, which multiplied by 4 turns out to be smaller in area then the original underlying polygon. 
I created the vector grid with the following set up. The grids are 2000m by 2000m.
I double checked this by adding an area field to the attribute table to check.
The whole underlying polygon is 1,019,761.79 km2. And the area of the sum of vector grids touching that polygon is 251889*4=1,007,556 km2.
Do the lines have thicknesses? Is that where the missing area has gone?
