curveA[t_] := {0, 4} + t {3, -4}
curveB[t_] := {8, 2} + t {0, -2}
curveC[t_] := {2, 2} + t {0, -2}

Show[{ParametricPlot[{curveA[t], curveB[t]}, {t, 0, 1},
   PlotStyle -> {Directive[{Red, Thickness[0.01]}]}],
  Graphics[{EdgeForm[None], FaceForm[Lighter[Blue]],
    Polygon[{{0, 4}, {3, 0}, {8, 0}, {8, 2}}]}]}, Axes -> True]
Show[{ParametricPlot[{curveA[t], curveC[t]}, {t, 0, 1},
   PlotStyle -> {Directive[{Red, Thickness[0.01]}]}],
  Graphics[{EdgeForm[None], FaceForm[Lighter[Blue]],
    Polygon[{{0, 4}, {2, 2}, {2, 0}, {3, 0}}]}]}, Axes -> True]