The area of the inclined surface is:

${\mathrm{A}}_{\mathrm{n}}=\mathrm{A} / \cos \mathrm{\theta }$

The normal stress on the inclined surface (i.e., the $\mathrm{n}$ face) is:

$$\begin{gathered} {\mathrm{\sigma }}_{\mathrm{n}}=\mathrm{N} / {\mathrm{A}}_{\mathrm{n}} \\ =(\mathrm{P} \cos \mathrm{\theta }) / (\mathrm{A}/\cos \mathrm{\theta }) \\ =\mathrm{P}/\mathrm{A} {\cos }^2 \mathrm{\theta } \\ ={\mathrm{\sigma }}_{\mathrm{x}} {\cos }^2 \mathrm{\theta } \end{gathered}$$

where ${\mathrm{\sigma }}_{\mathrm{x}} =\mathrm{P}/\mathrm{A}=$ the normal stress on a vertical plane (i.e., the $\mathrm{x}$ face).