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### How to calculate packing fraction or packing efficiency of two dimensional (2D) hexagonal packing solid atoms?

Hexagonal close packing:
The particles in every next row are placed in the depressions between the particles of the first row. The particles in the third row will be vertically aligned with those in the first row. This type of packing gives a hexagonal pattern and is called hexagonal close packing
Packing efficiency calculation:
(1) One sphere will be in constant contact with 6 other spheres hence coordination number is 6
(2) Side of hexagon is a and a=2r where r is the radius of atom (sphere) .
(3) Area of hexagon unit cell is 6*area of six equilateral triangles
(4) Area of atoms in the hexagon unit
Packing fraction (PE) , fraction of area occupied by spheres