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calculation of Effective area covered

[IMG]file:///C:/Users/anilvik/AppData/Local/Temp/moz-screenshot.jpg[/IMG][IMG]file:///C:/Users/anilvik/AppData/Local/Temp/moz-screenshot-1.jpg[/IMG]hello guys,

i am new to this forum, i have a problem with calculating the effective area. Please see the attached doc file for figure information. In the figures, circles arranged in triangular,square and polygon shapes.

Problem: how to calculate the effective area covered by the circle ( you can ignore the boundary circles that means consider only the shaded region). Now if you increase the number of circles on the each side( for triangle and square) then the number of circles inside shaded area increases.

can any body provide the proof for calculating the effective area or point out the links

To me it looks like it is already proved by somebody but i couldn't find out on the internet.

please respond quickly guys , it is very important

thanks

sehwag007