2 of 3 added 196 characters in body
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}]]]}]

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Use MaxCellMeasure -> .025 to get

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Use MaxCellMeasure->{"Area" -> 0.01} and RandomReal[] (in place of RandomReal[{.1, .8}] to get

enter image description here