Electric fields through parallelepiped

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Fluxthroughme
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I have taken my Gauss surface as the front of the shape, with [itex]E_1[/itex] coming through uniformly. I get the right answer for the charge inside the shape, but I'm unsure about b. I imagine a situation that I've drawn could be possible, but I've never seen it before, so I do not know. I'm thinking that the parallelepiped is going through one of the plates involved in an infinite parallel plate set up, with a single infinite plate above them. The two fields would combine as I have labelled, and would, by superposition, give the right total fields at the places they required. If anyone could let me know whether this is fine, or just nonsense, it'd be helpful. Thank you.
 
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If the field were due to charges outside the parallelepiped, what would be the total flux?