  The paper provides an elementary proof establishing a sharp universal bound
on the $(d-1)$-Hausdorff measure of the zeros of any nontrivial multivariable
polynomial $p:\mathbb{R}^d\to\mathbb{R}$ within a $d$-dimensional cube of size
$r$. This bound depends solely on the parameter $r$, the dimension $d$, and the
degrees of $p$.
