Sister Mary Augustine says that if the hex truly has 8' parallel to the ground with a 14' ridgeline, then the width of the side has to be 70/11 feet, which makes the tarp width on the ground closer to 4.95' on one side rather than 4.8'. She thought that was enough to go after you with her ruler, but I pointed out that these days she needs a passport to get back into the USA, and so I think I dissuaded her.
But I got to thinking that since not all "covered space" is created equal (your metric of coverage is bird's eye---straight down) what is really wanted here is a utility function that, for a given tarp, ascribes a "coverage" value to every point in the x-y plane. For example, the value could be the fraction of all rays in the positive z dimension with that point as the origin, which intercept the tarp. This is motivated by the idea of rain coming down. But then not all rays are equal in terms of threat, so the rays that are more likely to correspond to rain would be given more weight. Then to get the utility coverage you'd sum the coverage value over all points in the x-y plane.
There's a simpler way I'm sure. If any ideas come to me that can be easily conveyed (unlike the babble above) I'll jot 'em down.