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TriangulateMesh[MeshRegion[{{0, 0}, {2, 0}, {2, 1}, {0, 1}}, Polygon[{1, 2, 3,4}]], 
 ImageSize -> 900, MaxCellMeasure ->.1, 
 MeshCellHighlight -> {{2, _} :>   Directive[Antialiasing -> True, 
   EdgeForm[],ColorData["SolarColors"][RandomReal[{.1,.8}]]]}]

enter image description here

Use MaxCellMeasure -> .025 to get

enter image description here