{px0, py0} = {1/5, 2/5}; {px1, py1} = {1/10, -2/5};{px4, py4} = {9/10, -3/10}; {px5, py5} = {6/5, 9/10};

g10 = ListLinePlot[{{px0, py0}, {px5, py5}}, PlotStyle -> {Thick, Blue}]; g11 = ListLinePlot[{{px1, py1}, {px4, py4}}, PlotStyle -> {Thick, Blue}];

points1 = {{px0, py0}, {px5, py5}};

points2 = {{px1, py1}, {px4, py4}};

g10 = Graphics[{Thick, Blue, Line[points1]}]; g11 =
 Graphics[{Thick, Blue, Line[points2]}];

poly = Graphics[{Lighter[Orange],
    Polygon[Join[points1, Reverse[points2]]]}];

Show[poly, g11, g10, PlotRange -> All, AspectRatio -> 1/GoldenRatio,
 Frame -> True]

l1 = {{px0, py0}, {px5, py5}};
l2 = {{px1, py1}, {px4, py4}};
ListLinePlot[{l1, l2}, PlotStyle -> Directive[Thick, Blue], Filling -> {1 -> {2}}]

l1 = {{px0, py0}, {px5, py5}};
l2 = {{px1, py1}, {px4, py4}};
l3 = {{px1 + 1/2, py1 + 1/2}, {px4 + 1/2, py4 + 1/2}};(*I just make it*)

filler1[list1__, list2__, col1_, col2_, lthick_] := Graphics[{col2, Opacity[0.75], Polygon[Join[list1, Reverse[list2]]], Thickness[lthick], col1, Opacity[1], Line[list1], Line[list2]}, Axes -> True]

filler2[list1__, list2__, col1_, col2_, lthick_] := Graphics[{col2, EdgeForm[{Thickness[lthick], col1}], Opacity[0.75], Polygon[Join[list1, Reverse[list2]]]}, Axes -> True]

(*lthick is the line thickness*)

plot1 = filler1[l1, l2, Blue, Gray, 0.02]
plot2 = filler2[l1, l3, Green, Brown, 0.02]
Show[plot1, plot2]

pts = {{1/5, 2/5}, {1/10, -2/5}, {9/10, -3/10}, {6/5, 9/10}};

RegionPlot[ConvexHullMesh[pts], AspectRatio -> 1/GoldenRatio]

l1 = {{px0, py0}, {px5, py5}};
l2 = {{px1, py1}, {px4, py4}};
ListLinePlot[ Join[{l1, l2},
    {Reverse@#, #2} & @@ Partition[Join[Reverse@l1, l2], 3, 2, {1, 1}]],
  PlotStyle -> {Directive[Thick, Blue], Directive[Thick, Red], None, None},
  Filling -> {3 -> {{4}, LightBlue}}]