What is "areal capacitance?"
"Areal capacitance" is the same as saying "capacitance per unit of area." "Areal" is the adjectival form of the word "area." To confirm this, the meaning is obvious from the units given in the paper:


  A mean areal capacitance of \$ 0.36 mF/cm^2 \$ can be obtained from
  the slope of Figure 3c...


Here we see that for every \$1 cm^2 \$ of area, there is \$ 0.36 mF \$ of capacitance. 

To find the areal capacitance, divide the capacitance by the area.