How i can calculate area of polygon with java ??

hello
i've trouble with calculation polygon-area
is there any body who is good at calculation of shapes?
i explain my problem with pictures.
on piture2, i can calculate red-area of polygon with reference "http://www.cs.princeton.edu/introcs/33modular/Polygon.java.html"
but, i can't do it on picture1.
please help me and understand that i'm poor at english
picture 1.
http://myhome.naver.net/imsangchin/trace1.jpg
picture 2.
http://myhome.naver.net/imsangchin/trace2.jpg

Do you have a formula that generates picture 1?
If so, then you can use the basic formula for integration... take very very small steps and sum up all the steps, you can get as close as you like by making the steps sufficiently small.
If you don't have a formula to generate the picture, then you can do it by essentially counting the number of colored pixels in the shape and calling them any type of appropriate units or actually scaling converting them to inches or cm or what ever you are using. You can do this by just scanning across the image and counting how many pixes are on each line, then go to the next line. Do this for the entire image only counting the target color and then do your conversion.

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