Formula Tomfoolery for Dummies

equilateral triangle area

When it comes to any math more complex than 2+2=4, a lot of people either throw up their hands in despair or run screaming for the exits. We long ago figured out that any math "teacher" who has ever used the phrase, "It's intuitive" simply does not understand what it means to "not get it." On the other hand, plenty of freelancers claim to "get it," but don't. We can't be certain which camp Sciencing.com's Allan Robinson falls into, but we suspect it's the whole intuitive camp, based on his post, "How to Calculate the Area of an Equilateral Triangle."

Robinson penned this one back near the dawn of time when he still styled himself as Emmet Mcmahan [sic]. A careful and exhaustive reading of the text, with visits to the archived version via the WaybackMachine shows that Robinson's post was ultimately correct. Our problem with the text? It's so clumsily written that only someone with a firm grounding in math and a lot of patience could decode it.
We'll dispense with the usual jeers at how Allan/Emmet had to pad out his post with useless information about equilateral triangles and go straight for the jugular. Here's how  Robinson/Mcmahan derived the height of the triangle so he could plug it into the formula A = ½bh:

"Express h in terms of s. Using the right triangle formed in step 2, we know that s^2 = (s/2)^2 + h^2 by the Pythagorean formula. Therefore, h^2 = s^2 -- (s/2)^2 = s^2 -- s^2/4 = 3s^2/4 [sic]¹, and we now have h = (3^1/2)s/2. Substitute the value of h obtained in step 3 into the formula for a triangle's area obtained in step 1. Since A = ½ s x h and h = (3^1/2)s/2, we now have A = ½ s (3^1/2)s/2 = (3^1/2)(s^2)/4."

Yup, the formula for the area of an equilateral triangle with sides s is,

A = (s² * √3) / 4

It's too bad Robinson didn't (or, knowing DMS², couldn't) use the superscripts and other math symbols plus a few words to make his text readable. Perhaps Leaf will send the post to one of their cleanup team to rewrite it. We hope that worthy would chose a different example triangle, however. Robinson's example was,

"...an equilateral triangle with sides of length 2. A = (3^1/2)(s^2)/4 = (3^1/2)(2^2)/4 = (3^1/2)."

Again, technically correct, but IOHO, the fact that s² cancels with 4 to leave just √3 could be rather confusing to someone having trouble following the math. That's a Dumbass of the Day move, in our book.

¹ We have no idea why Robinson/Mcmahan used a double dash to indicate subtraction.
² DMS is Demand Media Studios, the parent of eHow, now known as Leaf Group, the parent of Sciencing.com. That website name still gives us the willies...

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