Consider an equilateral triangle $\Delta ABC$ in 3D with $A=(1,0,0)$, $B=(0,1,0)$ and $C=(0,0,1)$ as well as its mirror image $\Delta A'B'C'$ with $A'=-A$, $B'=-B$ and $C'=-C$. We assume that these triangles are "filled in" such that they can cast shadows under the light of a sun. Let the sun be infinitely far away in the direction $s\in\mathbb R^3$ such that it casts rays parallel to $-s$.
Depending on $s$, how much surface area of the triangles is lit and how much is shadowed?
I can, for a given $s$, project the triangles onto the plane $H_s$ through the origin with normal $s$, choose a coordinate system on it, use the Sutherland-Hodgman algorithm to clip both triangles with respect to each other and compute the area of the resulting convex polygon. Unfortunately, I have trouble finding an analytical expression for the area of this polygon depending on $s$.