Trapezoids for Geometry Dummies

Ummm, Audrey? these are hexagons, not trapezoids...

In case you haven't noticed, we tend to be rather dismissive of the Demand Media Studios (DMS¹) family of websites... well, they're the Leaf Group family now, but six of one, half-dozen of the other. That's because they so often allowed innumerate and scientifically illiterate liberal arts types to write about math and science in articles fact-checked by other scientifically illiterate and innumerate liberal arts graduates. Sigh. Well, today we have another example: BA and MA English graduate Audrey Farley, attempting to explain "How to Find Angles in a Trapezoid" at Sciencing.com.

Farley blew it in her second sentence:

"In geometry, a trapezoid is a quadrilateral (four-sided figure) in which only one pair of opposite sides are parallel. Trapezoids are also known as trapeziums."

We say "blew it" because the bit about trapeziums is not only superfluous, it's wrong in about half the English-speaking world (the statement's true in British English, but not in US English). Moving right along, Audrey favors us with such instructions as

"List the given measurements. You may be given the measurement of an angle or a base. Or, you may be given the measurement of a mid-segment, which is parallel to both bases and has a length equal to the average of the two bases. Use the given measurements to determine what measurements, if not the angle, can be calculated. These calculated measurements can then be used to calculate the angle."

Yes, Audrey, that's the beginning of the process. Now, how do I actually "calculate the angle"? Nope, not there... shouldn't there be something about trigonometric functions, perhaps? Or something even simpler, like this? But it gets better: Farley then starts regurgitating text from a Cliffs Notes:

"Recall relevant theorems and formulas for solving measurements of bases, legs and diagonals. For instance, Theorem 53 states that base angles of an isosceles trapezoid are equal. Theorem 54 states that diagonals of an isosceles trapezoid are equal. The area of a trapezoid (whether or not isosceles) is half of the lengths of the parallel sides multiplied by the height..."

But Audrey: nobody asked about the area! And finally, there's this rubbish:

"Use measurements, such as the area of the trapezoid, to calculate the height, leg or base that is shared by the triangle. Then solve for the angle using the rules of angle measurement that apply to triangles."

Wow: now that's helpful! In other words. Audrey, you don't know how to find the angles of a trapezoid, right? And since you decided to pick up a few bucks trying to explain how to do something you couldn't do yourself, don't you think you deserve a little reward? Like, perhaps, a Dumbass of the Day award? Sure, you do...

¹ Demand Media Studios, now known as Leaf Group, is the parent of eHow.com and all those niches.

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