Misleading formulation in "which area is greater?" question

Question

Questions involving area comparison in geometric figures often ask "which area is greater?". See for example, Which area is larger, the blue area, or the white area? and Is the blue area greater than the red area?.

Now the rule of thumb for these questions is often that the areas are equal. From my point of view when asked which area is greater, either Area$(A)>$Area$(B)$ or Area$(B)>$Area$(A)$ and these are the only correct options. But proof shows that the areas are equal.

Therefore, I find the formulation of the question very misleading. The question itself already pushes you towards a wrong assumption that one of the areas must be bigger. And the formulation of the "question" should not give any information about the "anwser", faulty or correct, right? Thus for me, the formulation of the question is insufficient.

My main question is: So why do these types of (insufficient formulated) questions exist?

Are they deliberately here to baffle people and show them how mathematics can proof surprisingly counter-intuitive results?

PS

I guess that not interpreting the question as a multiple choice, or interpreting "greater" in the question as "greater or equal" can convince myself that the formulation is correct. But my main question still remains. Also, if I am overthinking this too much, please do say.

Yes. The fact that the areas are equal is supposed to be a suprise. Of course, the first thing I thought when I read that question was "They are probably equal." — Steven Alexis Gregory, May 17 '18 at 10:37
vote to close - meta is probably a better choice for this sort of question. — achille hui, May 17 '18 at 11:13
@achillehui See my tag "meta-math". I thought this one was the right tag, someone can migrate it there? — Bo5man, May 17 '18 at 11:45

score 1 · Accepted Answer · answered May 17 '18 at 12:23

Certainly, there are rules to good riddling. For instance, in wordplay, you want to avoid using the components of the punchline in the setup.

"What do you get when you cross a cow and a trampoline?"

"A MILKSHAKE!" (credit: Funology.com)

That rule doesn't stop three-year-olds from regaling everyone within earshot with the oh-so-clever new joke they concocted.

"What do you get when you cross a cow with a girl?"

"A COWGIRL!"

Such a construction isn't at all satisfying. Indeed, sophisticated riddlees might not guess the answer, because they expect it to not include either "cow" or "girl". But youngsters just don't know, or care, about the nuances.

Bear in mind that a lot of math puzzles in circulation nowadays are click-bait posts on social media. Often, the creators (or, more likely, their plagiarists), like three-year-old comedians, just don't know, or care, about the nuances of puzzling, especially math-puzzling. So you get the kinds of annoyingly ill-posed formulations in the questions you reference. (It's possible ---perhaps even likely--- that the posters are intentionally "pranking" the reader with misleading captions.)

Here on Math.SE, you can do something about the problem: Edit such a question to allow the surprise option ... but without telegraphing it like a three-year-old. Change "Is the red area greater than the blue area?" to "Which shaded area is greater?" (subtly allowing "neither"), but not "Which is greater? red, blue, or neither?"

Otherwise, just deal with this stuff the way grammarians deal with "ur" and "gr8" and "could of" in their Twitter feeds: Grab a ruler to measure just how far that vein is bulging out of your forehead; maybe you'll break a record!

Anyway ... If you've overthought your question, then I've probably overthought my answer, so I'll stop typing ... but not before making this point:

Disdain for imprecise formulations is a desirable trait in a mathematician!

Misleading formulation in "which area is greater?" question

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