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14 Jun 2022, 14:30
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
82% (01:18) correct
18%
(01:38)
wrong
based on 33
sessions
History
Date
Time
Result
Not Attempted Yet
What is the area of ABCDE?
A. \(144 + 36\sqrt{3}\)
B. \(144 + 18\sqrt{3}\)
C. \(144 + 12\sqrt{3}\)
D. 162
E. 153
Attachment:
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14 Jun 2022, 14:55
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Bunuel
Two ways.
First, the way I would do it if I were taking the test: ballparking. It's fast, it all but eliminates the potential for a careless mistake, and it's stress-free. Get the right answer and move on to the next one!
We have a triangle attached to a square. The area of the square is 144. For the area of the triangle, let's just look at it. Is it 10% of the square? 25%? 50%? 75%? 90%? I don't know, looks like close to half but maybe just a little smaller. So the total area is something like 200? 210? Sure, let's look at the answer choices. \(sqrt{3}\) is roughly 1.7.
A. \(144 + 36\sqrt{3}\) 144+61=205 Keep it.
B. \(144 + 18\sqrt{3}\) 144+31=175 Too small. Eliminate
C. \(144 + 12\sqrt{3}\) Even smaller. Eliminate.
D. 162 Way too small. Eliminate.
E. 153 Way too small. Eliminate.
Answer choice A.
That took about 15 seconds.
Second, the "real math."
We have a triangle attached to a square. The area of the square is 144. For the area of the triangle, since angle A is 150 degrees, once we take away the 90 degrees that make up the square, we have 60 degrees for the triangle. Same thing at angle D. That means we have an equilateral triangle. The base is 12. If we split the equilateral triangle into two, we have two 30-60-90s, with length 6 opposite the 30 degree angle, which means the height is \(6sqrt{3}\). The area of the equilateral triangle is therefore \(\frac{1}{2}(12)(6\sqrt{3})=36\sqrt{3}\). So the total area is \(144+36\sqrt{3}\).
Answer choice A.
The math is easy, but I'm sure you can see how it's not out of the question to make a careless mistake by taking 6 instead of 12 for the base of the equilateral triangle. And wouldn't you know, if you make that little mistake, you end up with answer choice B and miss a question that you know how to do. I simply don't see the upside in doing the real math here. It takes longer AND it opens up a bigger potential for making a little mistake that costs points. Agree?
ThatDudeKnowsBallparking
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03 Jul 2024, 09:37
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A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
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A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
