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Finding the shortest distance of two points and an area

So I have a region defined by something like MeshRegion[{{0, 0}, {1, 1}, {2, 1/2}, {2, -1/2}}, {Line[{1, 2}], Line[{2, 3}], Line[{3, 4}], Line[{4, 1}]}], and two ...
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RegionPlot with FindMaximum

I don't understand why each time I'm launching this computation Mathematica buggs and I get a message from Windows that the Kernel stopped working... I'm trying to get a map of where the value of ...