Given a cuboid with lengths $L_{x}$, $L_{y}$, and $L_{z}$ (where $L_{x}$ is the length along the $x$ axis for a non-rotated cuboid), what would be the area of its projection on the $YZ$ plane if rotated about the $y$ and $z$ axes?
I have worked out that area for a rotation on just the $z$ axis is calculated by $L_{z}(L_{y}\cos\theta_{z}+L_{x}\sin\theta_{z})$, but the shape isn't a rectangle once both axes have a rotation.
