How to calculate packing efficiency of 2d structures

Here packing efficiency is the ratio of areas of circle/area of the square. 100%
each atom is surrounded by 4 atoms as each corner is shared by 4  unit cells.
atom per unit cell is 4/4 =1

    Area of one atom as a circle is pi.r^2
  Area of the square - a^2 = 4r^2
a = 2r (check image)
so  percent packing = (pi.r^2 /4r^2 ).100%= 78.54%