= Solution
The reconstruction matrix has area multiplier $|\det M|=44$. A bulk-terminated monatomic surface would therefore contain $44$ atoms in that projected cell, whereas the reconstructed top layer contains $46$. Its density increases by
$$
\boxed{\left(\frac{46}{44}-1\right)100\%=4.55\%.}
$$
The denser layer can reduce the large tensile surface stress and improve the outermost layer's preferred metallic bonding, at the expense of registry/domain-boundary and elastic costs. Surface atoms need not prefer exactly the same equilibrium spacing as bulk-coordinated atoms.
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