These segments can be many things!
Normal to the center of losange then move in their 4 places for intersection with the future growing plane from the losange
Vertical Z...
Inclined to a groundbase for be aligned at something...
etc...
all this will give slightly different results for your Plane following that you want ...

thanks again Pilou a manual process but logical will let you know how the project transpires hoping to make each panel a bolted together plate of steel.

Hi Pilou,

Having trouble with this section of workflow - trying to get the intersection of the lines and the planar surface.


Make boolean like this

Select 1 2 Call Boolean Isect 3 4 as "second object set"
(you can of course take more facets in a pass - in your case 7 vertical Quads selection)
that gives the 4 points for PolyLines then Planar...erase not wanted ...etc
But it's an hard work because only "manual"! ;)

The Boolean ISect are more for see and Keep Surfaces (or Volumes) Intersection!

So
By Default
Just select all lines
Call Trim
Click Plane
Points are shown for info to remove or not but hidden as soon as you valid the Trim!

Re-select the Lines and ask Show Points if you want to see them again for any reasons!
...

so with your file

thanks for you input Pilou much appreciated will send progress updates as it materialises.