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,
ramification (n.): ram-if-uh-kA-shun
further implications, branching effects or divergent consequences
|
and yet the mere mechanical exercise is worthwhile in that it is a relatively routine
maneuver
maneuver (n.): muh-nU-vuhr
a move made to gain a tactical advantage; a deliberate and coordinated movement requiring skill; a specific action executed as a training exercise
|
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
coherent (adj.): kO-hair-ent
marked by an ordered, logical and aesthetic relation of parts; clear and consistent; intelligently cohesive
|
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...