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If we take the documentation example for BoundingRegion and change "MinDisk" to "MinConvexPolygon" it no longer works:

pts = {{3, 10}, {6, 3}, {10, 2}, {2, 8}, {3, 3}};
BoundingRegion[pts, "MinConvexPolygon"]
Graphics[{{Yellow, %}, Point[pts]}, ImageSize -> Tiny]

gives the error:

"BoundaryMeshRegion is not a Graphics primitive or directive".

BoundingRegion[pts, "MinConvexPolygon"] does give a working Graphics object that I can use in plots. But how do I change the color in this case?

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You can use BoundaryMeshRegion to change the mesh cell styles:

BoundaryMeshRegion[
    BoundingRegion[pts, "MinConvexPolygon"],
    MeshCellStyle -> {2 -> Orange}
]

enter image description here

In Mathematica 12 BoundaryMeshRegion is supported as a Graphics primitive:

pts={{3,10},{6,3},{10,2},{2,8},{3,3}};
BoundingRegion[pts,"MinConvexPolygon"]
Graphics[{{Yellow,%},Point[pts]},ImageSize->Tiny]

enter image description here

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