# Everything I Know About Trapezoids

The set of posts about the area of a trapezoid seems to form a nearly coherent enough whole that it seems worthwhile to make a convenient reference point so that people searching for “how do you find the area of a trapezoid in the most convoluted and over-explained way possible?” have convenient access to it all. So, this is the path of that whole discussion.

How To Forget The Area Of A Trapezoid: The instigating event was my realizing in class I’d forgot how to prove the formula of the area of a trapezoid based on setting it up as the difference of two triangles.

Setting Out To Trap A Zoid: The first part in explaining the difference-of-triangles formula was therefore to come up with a drawing of a trapezoid, which started the discussion of how can one pick one trapezoid drawing from the many imaginable alternatives?

How Do You make A Trapezoid Right? continues the discussion of diagrams by showing some of the subtler assumptions commonly made in trapezoid-drawing — particularly, that the longer base is on bottom, or that the parallel bases are either horizontal or vertical — might not be the case, and goes on to explain how trapezoids can serve a role in finding the area enclosed by a curve, the start of integral calculus.

Drawing A Trapezoid’s Picture simplifies things to one generic-model trapezoid, with the non-parallel legs extended and the parts of the figure labelled. It spends its time explaining what the labels are, and to some extent, why the labels are those rather than other symbols.

The Difference Of Two Triangles shows how to use this diagram and the idea of taking the difference in area between two triangles to express the area of a triangle.

How Two Trapezoids Make This Simpler makes simpler and more general the proof of the area formula, by removing one of the assumptions needed for the difference-in-triangles scheme to work, and also by removing the need to think of properties of similar triangles.

Or, Work It Out The Easy Way makes the proof much simpler yet, by reducing the problem of the diagram and the trapezoid’s area to one of adding a line, splitting the figure into two triangles, and finishing everything in almost no time.

How Many Trapezoids Can You Draw? puts forth that question to any readers. There are some rules set down so that the answer isn’t a boring old “infinitely many”, but I don’t think they’re unfair rules.

How Many Trapezoids I Can Draw puts forth my answer, although on thinking it over I’m not sure that I shouldn’t have made it one more instead. I have to decide just how I feel about parallelograms, which is the sort of thing one worries about when one thinks too long about fine mathematics points like how many trapezoids there could be.