# How to fill a triangle enclosed by three non-parallel lines

I cannot understand how to fill the triangle, and only it, made by the given lines and the x-axis. Here is the code I have tried:

Clear[f, g, plot, reg];
f[x_] = -x + 6;
g[x_] = 2 x - 4;
plot = Plot[{f[x], g[x]}, {x, 0, 23},
PlotStyle -> {Darker@Cyan, Darker@Green}, AspectRatio -> Automatic];
reg = RegionPlot[{f[x] <= g[x] && y <= 8/3}, {x, 2, 6}, {y, 0, 8/3},
PlotStyle -> LightGray, BoundaryStyle -> None];
Show[reg, plot, PlotRange -> {-1, 5}, AxesStyle -> Arrowheads[{0.05}],
Axes -> True, Frame -> False]

whose output is as follows:

Any help? Thank you.

I was messing around with the functions f and g, but I cannot find a way to fill only the triangle.

• reg = RegionPlot[{y <= g[x] && y <= f[x]}, {x, 2, 6}, {y, 0, 8/3}, PlotStyle -> LightGray, BoundaryStyle -> None] Feb 12 at 23:53

f[x_] = -x + 6;
g[x_] = 2 x - 4;
h[x_] := Min[g[x], f[x]];
Plot[{f[x], g[x], h[x]}, {x, 0, 23},
AspectRatio -> Automatic,
PlotStyle -> {Darker@Cyan, Darker@Green, None},
Filling -> {3 -> {Axis, {None, Blue}}}]
Clear[f, g, reg];

f[x_] := -x + 6;
g[x_] := 2 x - 4;

reg = ImplicitRegion[y <= g[x] && y <= f[x] && y > 0, {x, y}];

p1 = Plot[{f[x], g[x]}, {x, 0, 8}
, PlotRange -> {-1, 4}
, AxesOrigin -> {0, 0}
, PlotStyle -> {Darker@Cyan, Darker@Green}
, PlotRangePadding -> {{0, 2}, {0, 0}}
];

p2 = RegionPlot[reg
, PlotStyle -> HatchFilling[]
, BoundaryStyle -> None];

gr = Graphics[{HatchFilling[], Rectangle[]}
, ImageSize -> Small
];

legend = LineLegend[{Darker@Cyan, Darker@Green, White}