the two trapezoid formulas yield the following:

P =	h + h + h + h	&	A =	0.5(h + h) × h
=	4h		=	0.5(2h) × h
			=	1h × h
			=	h²

Switching to the traditional variable "s" instead of "h" concludes our inspirational derivation of both (Perimeter & Area) formulas for a square:

P  =

4s

&

A  =

s²

That then takes care of our square (a third and final polygon) whose Perimeter & Area formulas are also encapsulated within the trapezoid!
     Mission accomplished?  The splendid details of all these foregoing derivations are secondary in importance to recognizing that the triangle, rectangle, and square are all transformations of the more general figure — the (totally terrible and terrifying) trapezoid.  Yikes...

In other words, the primary focus is to "realize" that each of the formulas for Perimeter & Area for each of  these three polygons are completely contained in the pair of trapezoid formulas:

P =	a + b + c + d	&	A =	12(b + d) × h

     Once this understanding is apprehended then remembering the Perimeter & Area formulas for a trapezoid are enough, i.e., one only needs to know two formulas (as opposed to eight).  And SO, this excruciating endeavor you've just encountered and just perhaps even ecstatically endured might actually seem worthwhile after all?  Alas no need to thank (or remunerate) me, grasshopper, for i am already paid handsomely in order to bestow enlightenment upon thirsty souls such as thyself.