The Geometry of Squares for Dummies

diagonal of a square

We spend a lot of time at the Antisocial Network browsing the niche sites where Leaf Group (the former Demand Media Studios¹) has stashed much of the content formerly found at eHow.com. Why? Partly because so many other content farms have gone tits-up and partly because eHow.com was the root cause of the "Panda update" at google that killed those content farms. The latter is mostly because of the quality of the content, content like "How to Find the Height of a Square," an Allison Horky production at Sciencing.com.

Here: let us tell you. Where h = the height of a square (in increasing order of complexity),

1. h = length of any other side of the square
2. h = perimeter of the square / 4
3. h = square root of the area of the square
4. h = (square root of the square of the diagonal of the square) / 2
5. h = diagonal of the square / 1.414^†
6. h = cos(45) * (length of diagonal) or h = sin(45) * (length of diagonal)

There you go: seven different ways to calculate the height of a square, none requiring more than ten words.

Horky fell victim to the format specifications of Demand Media, which demanded that she write 300 to 500 words in three to five steps. As a result, Allison found herself forced to go for the most complex of the six, the one that uses trigonometric functions. That's why she pounded out the following paragraph for her "Step One":

"Determine if you can use trigonometry to find the height of the square. You can only use trigonometry if you have the length measurement for the diagonal line that can divide the square into two equal triangles. You need three pieces of information to use trigonometry. Any combination of three angles or sides will help you find the other missing measurements for the remaining angles or sides. The two exceptions are only having the three angle measurements or having only one angle and two sides."

It appears that all those sociology courses Horky took were rather light on math, because that's not how trig works. The paragraph also gives short shrift to geometry, since (at least we'd hope) anyone who's passed eighth-grade geometry knows that the angles in a square are all 90 degrees. Whatever... Allison went on to explain "how to use trigonometry," taking her readers through almost 300 words to explain these seven:

h = cos(45) * (length of diagonal)

Along the way, Horky padded her "answer" out with such blather as,

"Set up your equation, where 'h' equals the unknown height of the square, and the hypotenuse equals 50. Cosine(45 degrees) = h/50"...

...which would have made much more sense to her readers if Allison had mentioned that she was using the example of "diagonal = 50"... After her tortuous path to getting the right answer by the hardest means, Horky cheaped out in her "tip," telling her readers that,

"You can also measure the height of the square, if it is sized correctly."

Now that she's done insulting our intelligence with that tip, we would like to present Horky her award: the Dumbass of the Day.

¹ It broke our collective heart when the company changed its name, because while it works to say, "You can't spell 'dumbass' without 'DMS," "without 'LG'" just doesn't work. Boo.
^† 1.414 is the square root of 2.

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