How Many Trapezoids I Can Draw

I guess this is a good time to give my answer for the challenge of how many different trapezoids there are to draw. At the least it’ll provide an answer to people who seek on Google the answer to how many trapezoids there are to draw. In principle there’s an infinite number that can be drawn, of course, but I wanted to cut down the ways that seem to multiply cases without really being different shapes. For example, rotating a trapezoid doesn’t make it new, and just stretching it out longer in one direction or another shouldn’t. And just enlarging or shrinking the whole thing doesn’t change it. So given that, how many kinds of trapezoids do I see?

Drawing A Trapezoid’s Picture

(It strikes me, this might just as well be Trapezoid Week here. )

Since I did work out the area of a trapezoid starting from the area formula for triangles, and since I was embarrassed to have not seen it sooner, I decide to share it here, where it may do someone some good, particularly if it’s me for next time I teach a class like this. The punch line is known far ahead of time. The trapezoid is a four-sided figure with two sides parallel. The parallel sides have lengths b₁ and b₂; they’re considered bases. The two bases are an altitude a apart. The area of the trapezoid then is a * (b₁ + b₂)/2.