/sci/ - Science & Math

I'm supposed to find the flux through the surface of this prism in a uniform electric field pointing along +x. I redrew the prism as a flat shape and added some colors here.
Flux through purple, green, and yellow should be zero because their normals are perpendicular to the field. Flux through blue should be [math]-EWH[/math], and flux through red should be [math]\frac{1}{2}EW\sqrt{H^2+B^2}[/math].
Why isn't the total flux zero? It's a closed surface with no charge inside. I'm imagining an infinite charge plate to the left of the prism generating the uniform electric field. It wouldn't matter what closed surface you rope off; there would be no charge inside it, so the total flux electric flux be zero.
The field also has zero divergence, so there's no charge density anywhere.