Solution
= Solution
The particle centre can move approximately $\ell-\sigma$ from the cell centre towards each of its four nearest fixed neighbours. Approximating the actual curved boundary by a square gives
$$
\boxed{a_c\simeq[2(\ell-\sigma)]^2=4(\ell-\sigma)^2.}
$$
This is the area accessible to the \b[centre], not the geometrical area enclosed by the fixed particle centres or an area computed using $\sigma/2$. Two equal particles must keep their centres at least $\sigma$ apart.