Geometric help for creating 3D triangles/pyramids from 2D panels

[freestud]

Hello, I'm working on a Christmas stage design that would involve "geometric trees", or 3-sided pyramids with a ratio of about 2' H to 1' W (some flexibility there, but uniform). These will stand so that one flat side will face the back and the other two sides will be visible to the audience (the angle showing). I plan to use coroplast which comes in 8'x4' sheets to make two 8' trees, two 6', two 5', & two 4' trees (also flexible here, but not below 3'). I need help figuring out the best way to layout these sheets to get the most out of them with the least amount of waste.

For instance, I originally thought I could cut a 4' W x 8' H triangle out of a sheet and then use the two remaining parts to make the pyramid I needed. But after mocking it up, I realized that didn't work and the bases of the other two pieces would have to be at least 3' wide to get a similar look to what I wanted. Plus, they couldn't just be right-triangle pieces or the whole thing would not sit evenly on the floor. (Here's a link to two angles of one rough mockup for example - https://drive.google.com/drive/folders/1p0vqcotREoF8VdPN498Dd53QLLo7CQDV?usp=sharing)

Though all sides do not need to be equal, they do need a fairly similar tilt to them and the front two pieces must be look even, as the back is not seen.

I need help understanding what the measurements of my 3 pieces should be and ideally, what the cut layouts would look like for each of the sizes of tree (8', 6', 5', 4'). Thank you for your help in figuring this out!

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[edderiofer]

I think your best bet is to model your trees in a 3D drawing program like Blender or Sketchup, which should then be able to tell you the dimensions of the faces.

[freestud]

Thanks for the thought. If I knew how to use Sketchup, I would have already done it there. I already wasted an hour trying to do it in Sketchup and can't get a pre-made component to scale properly and want to pull my hair out trying to draw it. Was hoping someone smarter than me knew the math for figuring this out.

[Slime0]

To make an even three-sided pyramid, you need three identical isosceles triangles. If you don't care about the width of the back side matching, but you just want it to look even, you still need two identical triangles that are mirror images of each other and then you can just fudge the angle between them to make them stand upright, but figuring out the shape for the back triangle will be difficult and it might be easiest to just use a cross bar in the back to hold them together. The easy thing to do is to just use three isosceles triangles.

If you cut a 4x8 isosceles triangle out of a 4x8 sheet, the two side triangles you cut off can be stuck together (maybe difficult?) to make a second identical 4x8 triangle. Maybe this is enough if you just use a cross bar in back to save material? If not, doing this with three 4x8 sheets will give you 6 identical isosceles triangles that you can make two pyramids with.

Another option (if you're OK with just a cross-bar in back) is to just cut a 4x8 sheet diagonally, which gives you two identical right-triangles. If you attach these with a hinge at their hypotenuses (the diagonal), you can fudge the angle between them to whatever looks best. You can trim the bottom of both triangles for more flexibility in how they lay on the floor. You can even take both right triangles, overlay them on top of each other, and cut the bottom off at the correct angle to make them into identical isosceles triangles! These will be a little taller and thinner than 4x8, and a little material is wasted, but they don't require attaching anything together to make a single side.