And although it may not yet be obvious from our latest results (which are)... 

P  =

2b + 2h

&

A  =

bh

Only a smidgeon of juggling remains to produce the intended outcome.  It involves substituting the typical (length) and (width) variables, "l" & "w" in place of "b" & "h" respectively, and after which we obtain the two traditional formulas for a rectangle:

P  =

2l + 2w

&

A  =

lw

     Both the triangle and rectangle have also manifested themselves as special cases of the trapezoid, and correspondingly both pairs of formulas (for the Perimeter & Area) have also been derived from the trapezoid formulas.  That's two down and one to go.  Time then to finally see how it is that a square is also a special case of the trapezoid.
     For a square, it is very much the same type of transformation as the one we have just seen with

the rectangle (in that the parallel sides need to coincide in horizontal position and length).  It needs also be the case that this pair of sides have their lengths match exactly the height of the trapezoid, regardless of whether that requires the shrinking or stretching of the sides (labeled "b" & "d," in the illustrations for each possibility). trapezoid transforms into square: sides "b & d" shrink to length "h" trapezoid transforms into square: sides "b & d" stretch to length "h" In either case, once the square is formed then, all sides are now the same length, meaning that:  a = b = c = d = h. Substituting the quantity "h" for all the other variables (a, b, c & d) in both of