Read coordinates from many files and calculate polygon areas
I couldn't run your code, so I can't say how much faster the following will be.

My suggestion is to use NumPy's loadtxt function to get the array of the necessary coordinates. With this function, you can specify skiprows and max_rows parameters to get the necessary rows, 36-45. This should be more efficient than reading all the file in memory. 

Here:


areaAr.append(PolyArea(x[36:41],y[36:41])) 
distance = max(np.abs(x[36]-x[39]),np.abs(x[42]-x[45]))
modifiedarea.append((PolyArea(x[36:41],y[36:41]))/distance)        



you calculate PolyArea two times, but it is enough to calculate it only once and then reuse the result. 

The final code could lool like this:

for filepath in df['filepath'].iloc[:10708]:
    values = np.loadtxt(filepath, 
                        skiprows=35,
                        max_rows=10)
    x = values[:, 0]
    y = values[:, 1]
    area = PolyArea(x[:5], y[:5])
    areaAr.append(area)
    distance = max(np.abs(x[0] - x[3]), np.abs(x[6] - x[9]))
    modifiedarea.append(area / distance)