Maljunulo,
Wasn't aware I'd used the word simplification, either above or in the linked thread. Checked, dont see it. I think the answer to your question is in the chart which calculated linear FOV at 50 yards (2 ways*) and square area at the same distance combined with the small crude chart i typed into the EL vs SF thread #13, quoted, above, that used 100 yards.
Excerpted from the latter at 100 yards, heres FOV and square area.
--------------FOV---------Sq Area---% bigger than EL
EL 1042------33.6'--------887sf------- -
SF 1042----- 36'----------1018sf-------15%
Nl 1042------39.9'--------1250sf-------41%
From the attached chart in #127 above, here's the data for 50 yards, without the SF 1042 as that seems not so relevant to your question, wasn't part of the thinking for that chart, and I'm feeling lazy.
--------------FOV---------Sq Area
EL 1042------16.8'--------221.7sf
Nl 1042------19.95'-------312.6sf
As to terms that others like to use like "3D Field of View," I get and share your confusion. Nor do I see how that relates to this bit of math. You can see you are correct as you go from 50 to 100 both the linear FOV and Square Area do get bigger. A diagram of this attempting to depict the idea, would reveal a cone. But we dont see a cone looking through a bino, right? We see a circle. Im less excited about the apparent slam dunk of square area over the common, industry used, FOV. I get the numbers are sure impressive, but as I tried to write in that ramble, the whole idea of square area as a 100% of the time used thing is less clear. This latter doesnt impact your question in 131, though.
*to the chart. Column E is 50 yard square area, the thing you were asking about. Columns C and K are the linear FOV adjusted to 50 and 100 yards, from Col B/1000 yards). Columns G-J as I wrote, were done for the fun of it, as I hadn't played with trigonometry in a while, and wanted to show that trig and simple percentage were essentially the same. See Col C and Col J. The difference here is from rounding off.
You wrote, the apex angle of which is quoted as FoV. That's correct it is the "apex" angle, (aka eyeball). But as we have FOV commonly used - the linear thing. This would then be angular FOV. (see col G).
Feel free to PM me if you want to discuss more.