Consider the problem of measuring the area of a lake, given a map. One smart way to calculate the area is to use a planimeter which works on the Green's theorem. Green's Theorem may seem rather abstract, but it is a great tool for finding areas of arbitrarily bounded regions. A person has decided to calculate the area of a lake given in the following figure. She started walking anticlockwise from point (1,0) around the lake and measured the vertices of the lake polygon as given in the figure. Use Green's theorem to calculate the area of lake.

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