Solution
= Solution
The <reciprocal lattice> of a triangular surface lattice is triangular, so its first <Brillouin zone> is a regular hexagon. Its area is one reciprocal primitive-cell area:
$$
\boxed{A_{\rm BZ}=\frac{(2\pi)^2}{A_s}=2.27537\ \text{\AA}^{-2}}.
$$
The zone has centre-to-corner distance $4\pi/(3L)$ and centre-to-side distance $2\pi/(\sqrt3L)$, consistent with this area. These reciprocal lengths use the convention $t_i\cdot b_j=2\pi\delta_{ij}$.