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Trivia (merged)

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PrincessPeach said:
The area of the bottom shape is not 33. It would be 33 only if there were not a 1-unit square gap. Because they are not triangles, you cannot use b*h/2 to calculate area, which, in you could calculate it, would equal 32.5.
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Sure it is. The sum of the colored shapes + 1 =33 units.
For the top shape, the area is just the sum of the colore shapes, 32 units.

b*h/2 would give 32.5 as the area for both shapes, but neither are triangles.
 
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vrbryant said:
The blue and red pieces are not proportioned such that conservation of matter applies. Put simply, the first collection of shapes does not form a triangle, but a quadrilateral. The area of both figures is the same, but neither is a triangle.
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you surely jest, vrbryant; otherwise, you don't know what a triangle and a quadrilateral are. the first is definitely a triangle. the second is definitely not a triangle (there is a chunk missing).

the answer requires a closer look. i was given this problem about a month ago. i found the answer via serendipidity.
 
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In order for the first shape to be a triangle, the slopes of the two smaller triangles would have to be equal. The slope of the red triangle is 2/5 (.4), the slope of the blue triangle is 3/8 (.375). BK - we are in agreement - neither shape is a triangle.
 
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OSU_Buckguy said:
you surely jest, vrbryant; otherwise, you don't know what a triangle and a quadrilateral are. the first is definitely a triangle. the second is definitely not a triangle (there is a chunk missing).

the answer requires a closer look. i was given this problem about a month ago. i found the answer via serendipidity.
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No, the top shape isn't a triangle. The "hypotenuse" is not a line. It is two distinct lines with different slopes. They want us to think its a triangle.
 
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OSU_Buckguy said:
you surely jest, vrbryant; otherwise, you don't know what a triangle and a quadrilateral are. the first is definitely a triangle. the second is definitely not a triangle (there is a chunk missing).

the answer requires a closer look. i was given this problem about a month ago. i found the answer via serendipidity.
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Huh? Neither shape is a triangle. A triangle is formed by three straight lines. Both objects have four straight lines, but the angle formed at the intersection of the line segments which are the hypotenuse of the blue and red triangles meet at an angle meant to approximate 180 degrees and therefore appear to be one straight line... but they are not.

Edit: Damn... got to wordy there and got beat to the punch.
 
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vrbryant said:
In order for the first shape to be a triangle, the slopes of the two smaller triangles would have to be equal. The slope of the red triangle is 2/5 (.4), the slope of the blue triangle is 3/8 (.375). BK - we are in agreement - neither shape is a triangle.
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I think we are in agreement on the answer, too. I think I'm looking at the question differently. I am treating the bottom shape like a quadrilateral (similar to the top shape) and seeing the empty square as a part of that shape, with a total area of 33 units. We are in agreement that the "hypotenuses" are not lines, but are, in fact, made up of two separate lines.

We also agree that the "hypotenuses" of the two shapes are not identical to one another. I'm willing to bet everything I own that the area between the two hypotenuses is exactly one unit.
 
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a ha. yes, on one hand the top figure is most definitely a triangle, inasmuch as a basketball is a sphere. however, a real life basketball can never be a true sphere, except only hypothetically.

therein lies the solution to the inconsistency.

again, the top figure is a triangle and not a triangle at the same time. it depends on your expectation of a triangle.

edit: also, the solution is gimmicky.
 
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OSU_Buckguy said:
a ha. yes, on one hand the top figure is most definitely a triangle, inasmuch as a basketball is a sphere. however, a real life basketball can never be a true sphere, except only hypothetically.

therein lies the solution to the inconsistency.

again, the top figure is a triangle and not a triangle at the same time. it depends on your expectation of a triangle.

edit: also, the solution is gimmicky.
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What? Am I missing something here? On which hand is the top figure a triangle? My 'expectation' of a triangle is that it be made up of three straight lines. It has already been proven that both figures are quadrilaterals, since the slopes of the small triangles are different, and therefore the 'hypotenuse' of each is actually two lines joined by an angle that is only close to 180 degrees. Under what hypothetical situation is that ever a triangle?

The puzzle is mere optical illusion. Gimmicky? Sure.
 
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