Needs["NDSolve`FEM`"];
r1 = ImplicitRegion[x^2 + y^2 <= 100, {x, y}];
r2 = ImplicitRegion[x^2 + (y - 5)^2 <= 4, {x, y}];
reg = RegionDifference[r1, r2];
bmesh = ToBoundaryMesh[reg, "MaxBoundaryCellMeasure" -> 0.5];
mesh = ToElementMesh[bmesh, MaxCellMeasure -> 1];
mesh["Wireframe"]

DynamicModule[{bL = 0.5, nn, bmesh, mesh, r = 10.2, mr, mcm, cL,
  x0 = -10, y0 = 7},
 bmesh = ToBoundaryMesh[reg, "MaxBoundaryCellMeasure" -> bL];
 mesh = ToElementMesh[bmesh];
 Column[{
   Row[{"Boundary Edge Length = ", Slider[Dynamic[bL, {(bL = # ) &,
        (bL = # ;
          bmesh = ToBoundaryMesh[reg, "MaxBoundaryCellMeasure" -> bL,
            AccuracyGoal -> 1];

          mesh = ToElementMesh[bmesh,
            MaxCellMeasure -> mcm]) &}], {0.05, 5},
      Appearance -> "Labeled"],
     "   Cell Area = ", Slider[Dynamic[mcm, {(mcm = # ) &,
        (mcm = # ;
          bmesh = ToBoundaryMesh[reg, "MaxBoundaryCellMeasure" -> bL,
            AccuracyGoal -> 1];

          mesh = ToElementMesh[bmesh,
            MaxCellMeasure -> mcm]) &}], {0.05, 5},
      Appearance -> "Labeled"]}],
   Row[{"Approximate Cell Edge Length = ",
     Dynamic[cL = Sqrt[mcm 4/Sqrt[3]]]}],
   Dynamic@
    Show[Graphics[{{Orange,
        Triangle[{{x0, y0}, {x0 + cL, y0}, {x0 + cL/2,
           y0 + cL Sqrt[3]/2}}], Line[{{x0, y0}, {x0, y0 + bL}}]},
       Circle[{0, 0}, r],
       Table[Point[r {Cos[n 2 [Pi]/nn], Sin[n 2 [Pi]/nn]}], {n,
         nn = Round[2 [Pi] r/bL]}]}, ImageSize -> 10 72,
      Frame -> True],
     mr =
      MeshRegion[mesh,
       MeshCellStyle -> {0 -> {PointSize[0.002], Red}, 1 -> Black,
         2 -> White}]
     ]
   }]
 ]

Lx = 20; Ly = 30;
coords = {{0, 0}, {Lx, 0}, {Lx, Ly}, {0, Ly}, {Lx/4, Ly/2}, {Lx/2, Ly/
    2}, {Lx/2, (3 Ly)/4}, {Lx/4, 3 Ly/4}};
ClearAll[makeBM];
makeBM[bL_] := ToBoundaryMesh[
   "Coordinates" -> coords,
   "BoundaryElements" -> {LineElement[{{1, 2}, {2, 3}, {3, 4}, {4,
        1}}], LineElement[{{5, 6}, {6, 7}, {7, 8}, {8, 5}}]},
   "RegionHoles" -> {{(3 Lx)/8, 5 Ly/8}},
   "MaxBoundaryCellMeasure" -> bL
   ];

DynamicModule[{bL = 0.5, nn, bmesh, mesh, r = 10.2, mr, mcm, cL,
  x0 = -5, y0 = 25},
 bmesh = makeBM[bL];
 mesh = ToElementMesh[bmesh, MaxCellMeasure -> mcm];
 Column[{
   Row[{"Boundary Edge Length = ", Slider[Dynamic[bL, {(bL = # ) &,
        (bL = # ; bmesh = makeBM[bL];

          mesh = ToElementMesh[bmesh,
            MaxCellMeasure -> {"Area" -> mcm}]) &}],
      {0.05, 5}, Appearance -> "Labeled"],
     "   Cell Area = ", Slider[Dynamic[mcm, {(mcm = # ) &,
        (mcm = # ; bmesh = makeBM[bL];

          mesh = ToElementMesh[bmesh,
            MaxCellMeasure -> {"Area" -> mcm}]) &}], {0.05, 5},
      Appearance -> "Labeled"]}],
   Row[{"Approximate Cell Edge Length = ",
     Dynamic[cL = Sqrt[mcm 4/Sqrt[3]]]}],
   Dynamic@
    Show[Graphics[{{Orange,
        Triangle[{{x0, y0}, {x0 + cL, y0}, {x0 + cL/2,
           y0 + cL Sqrt[3]/2}}], Line[{{x0, y0}, {x0, y0 + bL}}]}},
      ImageSize -> 10 72, Frame -> True],
     mr =
      MeshRegion[mesh,
       MeshCellStyle -> {0 -> {PointSize[0.002], Red}, 1 -> Black,
         2 -> White}]
     ]
   }]
 ]