Calculating Prism Volume for Geometry Dummies

Pentagonal prism

Our core tenet at the Antisocial Network is that internet freelancers shouldn't be "informing" their readers unless they actually know what they're talking about. It would be nice, for instance, if  woodworking advice came from people who know the difference between nominal lumber sizes and actual lumber sizes; or content on pollination were written by people who can spell "angiosperm" correctly without having to look it up. That's not the way it is; but if you spend much time at eHow.com, you'll learn that this was rarely true in the old days, and is questionable even in their more recent, niche-based incarnation. Case in point? Self-described college "instructor" Michael Judge, who did a bang-up (not) job of writing "How to Calculate Volumes of Pentagonal Prisms"¹ for Sciencing.com.

The stupidity of the plurals notwithstanding (eHow never changed their titles), this is pure junk. It's junk mainly because Judge disposes of a fairly complex question in less than 150 words. What do we mean? We mean that Mike doesn't bother to define his terms in the process: oh, sure, he gives us the basic formula (volume is the product of height and the area of the base). This is what Judge tells you to do:

Calculate the perimeter of the prism base using the formula P = 5(s), where s is the length of any one side of the pentagon. Calculate the area of the prism base using the formula A = (1/2)(P)(a), where P is the perimeter just calculated and a is the apothem of the base. Multiply the base area just calculated by the height of the prism. Well, we can't argue with that: as far as we can tell from our research (including Michael's single reference), this is correct. But there are some problems: for one, did you notice that Michael defines "s" as the "length of any one side of the pentagon"?  This means that his solution is only good for regular pentagons, but we'll let that slide. It's his use of the unfamiliar word "apothem" that caught our eye: WTF is an apothem? And how can you call this "instruction" if you don't define unfamiliar terms like this?

Not only did Judge not define the word, he didn't even link to a site that defines it,. We can, though: the apothem is the radius of the inscribed circle of a regular polygon. Had Michael bothered to say this, we might not have nominated him for the Dumbass of the Day award -- but he didn't; so we did.

¹ The original has been deleted by Leaf Group, but can still be accessed using the Wayback machine at archive.org. Its URL was   ehow.com/how_8148201_calculate-volumes-pentagonal-prisms.html

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