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the Perimeter whereas "s" times itself represents the Area.  Simply put — for any square
P  =  4s     (Perimeter)
A  =  s²      (Area)      
     The trapezoid is now the culmination, of our polygon crusade It is a quadrilateral (four-sided figure) which requires that at least two sides be parallel...
These two parallel sides are usually represented as having lengths "b" and "d" (see illustration above).  In addition to knowing both of their lengths the distance between them (a.k.a. as the height or altitude) needs to be specified, and is frequently denoted "h".  And yet once more, the Perimeter is nothing more than the sum of its (four) sides, "a," "b," "c" & "d."  As for its Area, that is defined as the average of the parallel sides (i.e., the one-half the sum of "b" plus "d") multiplied by the height.  Thus, we have as our two corresponding formulas for a trapezoid as...
P  =  a + b + c + d      (Perimeter)
 

A  =  0.5(b + d) × h     (Area)      
     Before moving along to our fifth and final 2-D figure (the circle) a few observations about the inter-connectedness of triangles, rectangles, squares and trapezoids seem in order.  First, take notice of how the Area & Perimeter formulas for a square are just a special case of the rectangle where both the length and width are the same.  If one substitutes "s" for both l & w, we should see the following results:
P  =   2l + 2w & A  =   l × w
 =   2s + 2s  =   s × s
 =   4s  =   s²
This demonstration is not dramatically important in its ramifications, and yet the mere mechanical exercise is worthwhile in that it is a relatively routine maneuver to subsitute one expression for another to see where any simplifications may lead.  If you have had an algebra course in recent memory then this type of process probably should seem somewhat familiar (i.e., coherent and non-mysterious).  If not, look at it again just to see that it makes logical sense (without feeling any need to worry about having to recall what was done).
     Next, we will carry this very sort of algebraic practice a bit farther in order to see that each of the first three polygons  —  the triangle, the square, and the rectangle — are all indeed individually a special case of the trapezoid...
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