Great article, wonderful introduction to quadratic equations.
I had exactly the same difficulty - and after over 50 years my school maths is really, really rusty.
There must be a good reason as to why they chose those particular ways of denoting base and height of the triangle (rather than just b and h), and I assume it is correct. Still do not really understand that bit.
However if you use those expressions in the area formula for a triangle (area = half base time height) then it does come out.