Jennifer, I used to be a carpenter. As such, I usually figure any angles with a board and a rafter framing square. Basically, it is possible to calculate all this but the formula is not worth calculating if you have a square with a full set of tables. Lacking a square with a full set of tables, you can use something like this: http://planetcalc.com/1147/ (Very simple to use.)
Anyway, for a typical pyramid, the hip calculations are:
10ftx10ft@45 degrees:
Wall length length: 7.07ft
Corner/Hip length: 8.66ft
Total height at center: 5.00ft
9ftx9ft@45degrees:
Wall length length: 6.3640ft
Corner/Hip length: 7.7942ft
Total height at center: 4.5000ft
For 8.5ftx8.5ft @ 45degrees it is:
Wall length length: 6.01ft
Corner/Hip length: 7.36ft
Total height at center: 4.25ft
The odd lengths do not well correspond to the width of a 5ft wide piece of silnylon (or other materials) though. This is usually OK, since the peak actually needs extra stitching for some sort of pole pocket and vent openings/rain shield needed.
http://www.1728.org/volpyrmd.htm allows you to calculate multiple sides, 5, 6 or 8 is common. But, this is a bit harder to use. You can figure it out, I think.
Other Notes:
For “half” “Mids” such as the Z-Packs, you undoubtedly want beaks. These are actually just segments of the original calculations. The closer the tent skin is to your face, the more it will condense water. If your feet touch the tent, they WILL get wet. Generally, 16″ is about the minimum clearance wanted. I like 24″. The more shallow angles require longer “running lengths” but can make the thing a little lower in the center. 45degrees is a good compromise angle for clearance and width. I believe Z-Packs uses about 46-48″ as a center height. For me, this is awkward. My staff only measures 43-44″ and is a fixed length. Measure your staff to prevent fiddling with it. Typically a “Mid” will require more height than a single staff will provide. Just some random thoughts…