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][1]][1]

Use `MaxCellMeasure -> .025` to get

[![enter image description here][2]][2]


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

[![enter image description here][3]][3]


  [1]: https://i.stack.imgur.com/47P27.png
  [2]: https://i.stack.imgur.com/Q5xIq.png
  [3]: https://i.stack.imgur.com/nsWVn.png