Calcolo l'area (della sola penisola) usando le coordinate (latitudine, longitudine).  Poi la trasformo in km^2 tenendo conto che 1 grado di latitudine è 111 km (valore arrotondato) e che 1 grado di longitudine in Italia è mediamente circa 79 km.  Quindi calcolo area*111*79, e poi arrotondo il valore.

x = [8,7.87,7.6,7,6.81,6.81,7.2,7.08,6.6,6.6,7,6.82,6.82,7.7,7.7,7.5,7.5,8,8.15,8.47,8.7,8.8,8.9,10.1,10.25,10.45,10.5,10.46,10.75,10.73, 11.2,11.05,11.1,11.2,12.2,13.1,13.8,14.1,14.2,14.4,14.5,14.35,14.75,14.9,15.35,15.55,15.65,16.15,16.2,16.23,16,15.83,15.9,15.6, 15.65,16,16.6,16.58,17,17.1,17.18,17.125,16.8,16.52,16.5,17,17.2,17.2,17.82,18,18.36,18.5,17.9,15.9,15.87,16.25,16.2,16.1,15.1, 15,14.23,13.55,12.4,12.28,12.5,12.5,12.2,12.3,13.1,13.5,13.8,13.8,13.9,13.85,13.6,13.55,13.6,13.5,13.6,13.4,13.65,12.45,12.1,11.5, 11,10.5,10.4,10.1,10.05,10.2,10.05,10,9.6,9.5,9.3,9.3,9,9.1,8.95,8.85,8.4,8.45,8.1,8]
y = [46,45.9,45.95,45.85,45.81,45.7,45.35,45.2,45.1,45,44.6,44.5,44.35,44.12,44.08,43.9,43.8,43.87,43.9,44.3,44.38,44.4,44.38,44,43.84, 43.3,43,42.92,42.88,42.8,42.5,42.4,42.35,42.38,41.8,41.25,41.175,40.75,40.8,40.7,40.65,40.55,40.65,40.3,40,40.1,40.1,39,38.91,38.8, 38.72,38.6,38.45,38.25,37.85,37.9,38.45,38.75,38.91,38.89,38.95,39.4,39.6,39.65,39.77,40.5,40.5,40.4,40.28,40,39.75,40.1,40.7,41.5, 41.6,41.75,41.9,41.96,41.94,42,42.45,43.63,44.2,44.78,44.8,45,45.25,45.43,45.6,45.75,45.65,45.55,45.6,45.7,45.8,45.83,46,46,46.2, 46.3,46.5,46.68,47.1,47.05,46.78,46.81,46.5,46.6,46.45,46.28,46.2,46.35,46.3,46.5,46.5,46.35,46,45.8,45.8,46,46.25,46.4,46.28,46]

n = x.length-1
area = (y[n]+y[0])*(x[n]-x[0])
for (i=0; i<n; i=i+1) area = area + (y[i]+y[i+1])*(x[i]-x[i+1])
area = area/2; document.write(area)
document.write("<br>area = ",Math.round(area*111*79)," km^2")
document.write("<br>area = ",Math.round(area*111*79/1e4)*1e4," km^2")

Ottengo:
28.593575000000122
area = 250737 km^2
area = 250000 km^2

Il calcolo dell'area (senza la trasformazione in km^2) con lo script "area polig":

È calcolato anche il centroide, che con WolframAlpha trovo essere Città di Castello: