Remove["Global`*"]
(* 2.5 *)
xv={7.4,12.8,17.6,21.5,24.0,27.1,30.2,32.5};
yv={4.2,2.4,0.6,4.0,6.0,4.7,1.8,-0.6};
data=Transpose[{xv,yv}];
pl =Plot[Interpolation[data,Method->"Spline"][x],{x,5,32.5}];
lp=ListPlot[data,PlotStyle->{Red,PointSize[Large]}];
Show[{pl, lp}]
(* 2.6, 33.3 ?*)
Print["Estimated length: ",(∑_(i=1)^7)(Sqrt[(xv[[i+1]]-xv[[i]])^2+(yv[[i+1]]-yv[[i]])^2])]