According to F.5.1, A is the total required compression area at the roof-to-shell junction, or if you prefer, it is the "compression ring area".
The actual A is a geometrical calculated area- however the boundary of area came from other considerations not explained in API 650, only the rules to calculate A are given in Figure F-2.

In case you are interested on the derivation of the formula, it starts with the calculation of the failure pressure. The failure of the roof-to-shell junction can be expected to occur when the stress in the compression ring area reaches the yield point. This "compression" effect is in a horizontal plane because the roof force (along the tangent at θ angle) can be separated into two forces as the horizontal one, H and the vertical one, V.
The compression force is H (the biggest one) and the vertical force is just V=H*tan(θ).

Pf is given by the roof equilibrium equation on vertical, that's why DLR come into discussion, as well the V force and Pf*PI*D^2/4.
In SI units the failure pressure would be expressed in SI units as:

Pf=8*Fy*A*tanθ/D^2+4/PI*DLR/D^2 - units in [Pa]
(where A is the area subject to stress Fy)

or

Pf=Fy*A*tanθ/(125*D^2)+0.0012732*DLR/D^2 in [kPa]

In order to calculate the correlation between P=the internal design pressure and area A, API considers a safety coefficient of 1.6 applied to the pressure effects term (i.e. the first term), so the maximum design pressure, P is written as:

P=Fy*A*tanθ/(1.6*125*D^2)+0.0012732*DLR/D^2=
=Fy*A*tanθ/(200*D^2)+0.00127*DLR/D^2
which is API 650 F.4.1.

Mathematically this is equivalent with F.5.1.

Best regards.