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def area_by_shoelace(x, y):
   
"Assumes x,y points go around the polygon in one direction"
   
return abs( sum(i * j for i, j in zip(x, y[1:])) + x[-1] * y[0]
               
-sum(i * j for i, j in zip(x[1:], y)) - x[0] * y[-1]) / 2

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