Shading an area enclosed by a loop

I am plotting the folium of Descartes as a parametric plot, and trying to find the arclength and the area enclosed by the loop. I got both of them covered result-wise, but my professor wants us to shade the area enclosed by the loop, and bold the arclength(the whole loop). I have been trying to figure that out for quite some time now but just can't seem to get it to work.

1. One way I found out you can do that is by using RegionPlot[] and fill the parameters. In my case nothing is shaded just my plot is being printed. Link

2. I found this question on here Link but I didn't find it helpful, because some of the solutions include Filling which is not available for ParametricPlot[]

My code:

x[t_] := (12 t)/(1 + t^3)y[t_] := (12 t^2)/(1 + t^3)

Vertical tangent lines

dir = {0, 1};sol = Solve[Det[{{x'[t], y'[t]}, dir}] == 0, t, Reals];

Plot with the "shaded area" that doesn't work

Show[ParametricPlot[{x[t], y[t]}, {t, -100, 100},   PlotRange -> {{-10, 10}, {-10, 10}}, AspectRatio -> Automatic,   PlotStyle -> Red, AxesLabel -> {"x", "y"},   PlotLabel -> "Folium of Descartes",   BoundaryStyle -> Directive[Red, Thick]],  RegionPlot[  ParametricRegion[{x[t],     y[t]}, {{t, 0, Infinity(*sol = 0.793701*)}}],   PlotStyle -> LightBlue, BoundaryStyle -> None]]

It also wouldn't accept sol as an argument. I could be wrong but I think I am supposed to integrate from t = 0 to t = Infinity and not t = sol (0.739...) right?

As for the bolding part of the graph I was thinking about just using Style and Bold for an interval of values for t where they make a loop. Would that work?

Any kind of help is appreciatedThank you!