what size tarp negates use of bivy? and other interesting questions :)

10 feet long. That one extra foot over 9 feet really helps for bad weather.
That gives you 2 feet at your head and toes.
Even if you get a bit of splatter, keep in mind a tarp is well ventilated and there is usually a slight breeze going through, so your bag can dry out reasonably well.

You aren't going to save much weight over a pyramid with an appropriately sized tarp unless you are like me and don't use trekking poles. It's about versatility, which you don't get with a cat cut.
A-frame pitched low for storms, pitched high as a canopy with lots of room, easy pitch lean-to for roominess while blocking wind from one side, plow point pitch for 3 sides of wind protection, lots of options there. Perfect for use with a large warming fire.

1. For flat tarp most might say 8 x 10. A few might go for 9 x 7.

2. Any size shaped tarp with full coverage low-ish to ground that gives you enough room to sleep.

8×10 for a flat tarp. That size allows alternate pitches too. IMHO, everyone should have a flat tarp in the gear locker. If you want to experiment, get a poly tarp and head for the back yard.

Cat cut and other shaped tarps are usually limited to one pitch. They are better in the wind

The addition of beaks or other end pieces can make a smaller tarp more weathery. If you keep extending those ends, you end up with floorless tents. Put a hood on one and you have a Gatewood Cape :)

I plan on water coming in at a 45degree angle. So, the size will vary with the exact pitch. If you like a 40" high pitch, a 9' long tarp about 8' wide will do (assuming you use about 8" guy-lines on corners for ventilation.) I sleep towards the back, so there isn't a lot of "dry" space left.

In storm mode with heavier swirling winds, I plant one end tight and leave the other at a 3' height. This means only 3' will spray in. I put my rain jacket as a door and ignore the weather. Let it rain. If I have chosen a good piece of ground, and my tarp is well anchored, I have never had it blow out on me in 50-60mph winds. Usually you can tell before the sun goes down. (Edit: It sheds wind in three directions very well, but can catch wind if the door is into the wind.)

I don't bother with a trapezoidal tarp. Too many other problems setting it up. Stick with a standard square or rectangular tarp.

Cat Cuts are a bandaid for poor design, poor materials, and/or poor set-up:

If a tarp is set up properly, with heavy elastic guy outs, it will "pull" itself taught to compensate for any stretching. http://gossamergear.com/wp/diy-self-tensioning-guy-lines-2 (Edit:Basically a 4" loop of heavy elastic pulled taught. Cat cuts are really not needed for this.)

If it is designed in, you are limited in pitching options. (Though it is possible to "simulate" a pitched tarp with longer "poles" to set it up as a lean-to.) It does not really limit you, but it makes setup more difficult.

If you have poor materials, they will absorb more water than good materials. A silicone fly with a light coating of silicone will absorb a bit more water than one with a heavier coating. 1.2 and 1.3oz fabric is not real great. I use a thinned mix of mineral spirits/100% silicone caulk for about a .2-.3oz increase in fabric weight to improve this. The tarps stretch very little after 24hours in the rain…maybe as much as 4-5%, not 10% like out of the box.

Generally, a full coverage tarp will weigh about 1 pound including stakes and guylines. This will vary, of course. I have one that is about 12 years old that I have recoated three times that weighs about 17oz without stakes. A new one weighs about 13-14oz, depending, and cost about $60. (Edit: A new, factory made tarp will run close to $90) Cuben would weigh about 8-9oz and cost about $400. The silnylon also packs a bit smaller, it fits into my grease/cook pot.

6.5' X 8.5'

That's what my Brooks Range Ultralight Mini Guide Tarp measures. Perfect size for solo camping. Comes with 16 perimeter tie-outs and a center pull. Weighs 10.1 oz seam sealed and it's made of 20d calendered ripstop (a tad lighter than 30d).
Also comes in woodland camo, which is great for stealth camping. Not as roomy as a 7' X 9' or 8' X 10', but I can pitch it lower, it catches less wind and it only needs a small footprint.

I find that if I use 12 tie-outs I can get a rectangular tarp as taught as a cat cut. I can also pitch it closer to the ground, or directly to the ground to provide better protection in storm mode. Can't do that with a cat tarp.

I'll ditto that 8×10 is among the safer bets although I would feel fine facing a storm with nothing buy my Grace Solo.

"catenary cut? or does that also limit the pitch to A-Frame?"

Yeah for the most part but you can still get creative with it by staking it down to the ground on one side but leaving the other side higher for views as one example.

Cat cut is fine but if I were to recommend one tarp that would benefit the most people in most conditions, it would be a plain ol' 8×10 flat tarp.

Thanks Gents- great info! I think I'll forego cat cut and trapezoids for the mean time and look at flat tarps. Sounds like 8×10 as a sure bet and possibly even 7×9. I'm going cuben with this one, looking to put together a 5-ish # kit :)

Years ago I used to use a regular tarp from the hardware store. They're not that heavy and it's a good way to try out the whole tarp thing.

I have an 8×10 Equinox tarp. The nice thing about it is that it's big enough for two. It can be set up a lot of different ways, too. It's maybe not the lightest thing out there. Cuben would be way better. No stretch, quick dry and light.

Shaped tarp