= Solution
Since $B_{\rm hex}<B_{\square}$, the hexagonal lattice has larger accessible cell area at any common allowed total area $A>B_{\square}$. Hence
$$
\boxed{F_{\rm hex}<F_{\square},\qquad S_{\rm hex}-S_{\square}=Nk_B\ln(a_c^{\rm hex}/a_c^{\square})>0.}
$$
The kinetic entropies cancel at the same temperature. \b[The triangular lattice is favoured and has higher <entropy> within this cell model], even though both structures look ordered. More efficient packing leaves more local displacement freedom at a fixed number density. This comparison does not by itself establish whether either crystal is stable against the fluid.
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