They're dumb.
So.... if I understand you correctly... you're going to cut four trapezoids, with a top dimension equal to the length of the top square/rectangle piece, and a bottom dimension equal to... whatever the math says it is (I figure the top dimension is x, the height is h, and because you're working with 45
o angles, your base is x+2h).
You want to know what the angle from the face to the back is on the sides, so that when you fit all four together, the edges are flush all around on the outside and the inside.
If height h=0, then the that angle - from the face to the edge - would be 90
o. If height h was infinite (meaning the side trapezoids weren't trapezoids, but were rectangles), that angle would be 45
o. So if you're tipping the trapezoids on a 45
o angle themselves, wouldn't the face to edge angle be halfway between 45 and 90, or 67.5
o? I'm sure there's math to calculate that, but it's beyond me; you're probably better off taking a couple pieces of wood and test cutting them for fit.
(Holy crap, this would be so much easier in person or with a white board; trying to put this into words is a task in itself.)