  We show the analogy of Cauchy's surface area formula for the Heisenberg
groups $\mathbb{H}_n$ for $n\geq 1$, which states that the p-area of any
compact hypersurface $\Sigma$ in $\mathbb{H}_n$ with its p-normal vector
defined almost everywhere on $\Sigma$ is the average of its projected p-areas
onto the orthogonal complements of all p-normal vectors of the Pansu spheres
(up to a constant). The formula provides a geometric interpretation of the
p-areas defined by Cheng-Hwang-Malchiodi-Yang [9] in $\mathbb{H}_1$ and
Cheng-Hwang-Yang [7] in $\mathbb{H}_n$ for $n\geq 2$. We also characterize the
projected areas for rotationally symmetric domains in $\mathbb{H}_n$, namely,
for any rotationally symmetric domain with boundary in $\mathbb{H}_n$, its
projected p-area onto the orthogonal complement of any normal vector of the
Pansu spheres is a constant, independent of the choices of the projected
directions.
