Visualize Mesh Properties 

Using HighlightMesh, mesh properties can be easily visualized.

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X mesh2d = DelaunayMesh[RandomReal[1, {200, 2}]]

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Shade each face based on its area.

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X {minArea, maxArea} = {Min[#], Max[#]} &@ PropertyValue[{mesh2d, 2}, MeshCellMeasure]; Legended[HighlightMesh[mesh2d, Style @@@ ({{2, #}, ColorData["SunsetColors"][ Rescale[PropertyValue[{mesh2d, {2, #}}, MeshCellMeasure], {minArea, maxArea}]]} & /@ Range[MeshCellCount[mesh2d, 2]])], BarLegend[{"SunsetColors", {minArea, maxArea}}]]

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Shade each face based on its quality.

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X {minQual, maxQual} = {Min[#], Max[#]} &@ PropertyValue[{mesh2d, 2}, MeshCellQuality]; Legended[HighlightMesh[mesh2d, Style @@@ ({{2, #}, ColorData["SunsetColors"][ Rescale[PropertyValue[{mesh2d, {2, #}}, MeshCellQuality], {minQual, maxQual}]]} & /@ Range[MeshCellCount[mesh2d, 2]])], BarLegend[{"SunsetColors", {minQual, maxQual}}]]

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