I've read white papers claiming that square microstrip antennas have more desirable impedance matching characteristics and less side-lobe radiation than do circular microstrip antennas. Not wanting to repeat tedious simulation work to verify results, I simply apply the findings in faith. There...
Do a dimensional analysis.You may find a (time)^-3 term, which is a hint. Just as a wild guess, try units for area for A... then look up the dimensions for power.
Quite often, power ratios are expressed as a logarithm.
Circuit design, and especially PCB design, is a sort of "black art", like Voodoo. Textbook circuit design methods are used to choose "what components to use", but experience will tell you which circuit "topology" will strongly depend on precise component values and parameters, and which are more...
Demonstrate. Assign a different node as reference, assign it some ridiculous value (e^i*h maybe), rework the problem carrying the ridiculous term through all the arithmetic, and get the exact same answers.