find the proportional area of some squares confined betwnn a ring in C#

Question

Hi
Could any one help me solve this problem- the related picture has been uploaded, please look at that first.
I have a regular cartesian grid with known dimensions. then I will superimpose an annular ring ( two concentric circles with known radius). I want to find out the AREAL proportion of ALL squares(grid) which fall inside the annulus, separately.FOR EXAMPLE,  If you open the file, I want to obtain the area of each coloured part of squares and print them to a TEXT file.
Thanks