Three sided coin ( basic math question)

Feb 2018
In this PDF there is a comparison of different models describing 3-sided coins.

Now,on page 3

Model 1 is pretty clear, to calculate the probability (of the flipped coin landing on its side )
they consider coin side surface area to the total surface area ratio.

Model 2 is a bit confusing

it seems that they divide one side of a perimeter (h) by the sum of three other sides 2(2R)+h
rather than the sum of all four sides
intuitively it should be 2(2R) +2 h

What am I missing ?

Related question: how do they define cross sectional length?
Is it just a half of the diagonal, as per drawing?
And if that's the case,why would the probability be proportional to that length?
I don't find it very intuitive.

Jan 2018
Seattle, WA
A three-sided die, viewed from one 'end,' similar in shape to a slice of orange.