Let there be a geometric shape $\Omega$ of area $S$ lying in a plane $B$. Let the horizontal plane (the plane $xy$) be $A$. Let the angle between the planes $A$ and $B$ be $\theta$.
It could be easily proved that $AB \cos \theta$ is the length of the orthographic projection of any segment $AB \in \Omega$.
How can it be proved that $S' = S \cos \theta$ is the area of the orthographic projection of the shape $\Omega$ onto the plane $A$?