By Jackie, Researcher

Area of discussion: Intelligence Quotient [IQ]

Function of this discussion: To test our brain’s IQ

Requirement(s): Basic Mathematics’ skills involving area calculations

*The objective of this post is to share an extremely tricky question related to IQ and see whether could we solve this question together. Besides, it allows us to share the conflicts or perhaps some weaknesses in Mathematics’ theories. By having different comments and opinions from different people will greatly help to solve this problem faster.*

**Introduction**

Guest what? I saw this on my Facebook, and yet no one can give an
accurate or reasonable explanation on why this could happen. So, I took this
opportunity to share out to a larger crowd to see whether it could be solved or
not?

**My arguments:**

I know there is a difference of 1 unit²
between the first triangle and the second triangle, but I am going to tackle
them separately as the confusion already exist if we tackle either one of them even
without the existence of the other triangle.

**(The triangle at the top)**

According to Mathematics’ theory:

Area of a triangle

= 0.5(length x height)

= 0.5(13x5)

=
32.5 units²

But this is different if we calculate it one-by-one, all the four shapes
together:

Red: 0.5(8x3) = 12 units²

Orange: 7 units²

Dark green: 0.5(5x2) = 5 units²

Light green: 8 units²

Total : 32 units²

Why is there a difference of 0.5 unit²
exist?

**(The triangle at the bottom)**

According to Mathematics’ theory:

Area of a triangle

= 0.5(length x height) – 1 (note: minus one for the missing unit)

= 0.5(13x5) – 1

= 31.5 units²

But this is different if we calculate it one-by-one, all the four shapes together:

Red: 0.5(8x3) = 12 units²

Orange: 7 units²

Dark green: 0.5(5x2) = 5 units²

Light green: 8 units²

Total : 32 units²

Again, why is there a difference of 0.5 unit² exist?

I know some of you may argue that one of the triangles is concave, and
the other is convex (or perhaps the triangles are bend at the hypotenuse, but
this is not important anymore if we treat them as a separate IQ question. This
is because the difference in calculation of 0.5 unit² already arises even if we did not compare the
first triangle at the top with the other triangle at the bottom. Therefore, is
the calculation wrong? Or is there a conflict between calculating one-by-one
method and calculating by using Mathematics’ formula related to triangle?

The calculation is definitely wrong. Without even comparing the two triangles, it is still visible that the "triangle" shown on top is not a triangle. Hence, calculating its surface using formula for calculating the triangle is wrong.

ReplyDeleteFirst, allows me to define what this triangle, using standard polygon. A triangle is a polygon with 3 straight sides, and 3 angles. The diagram above have 4 straight sides when placed together, thus creating 4 angles; 3 acute, 1 reflex. This in turns, means that the shape does not falls under triangle.

Second, we can calculate that even from the first shape that there will be 0.5 units difference. One way of doing this is to treat it as a regular triangle, and double it to get a rectangle. It can be illustrated in the calculation below.

Supposed area of rectangle created by two "triangles" shown in first figure

= 13 x 5 units

= 65 units

Actual area covered by "rectangle" created by first diagram

= 2(0.5(2 x 5) + 0.5(3 x 8) + (7) + (8))

= 64 units

Since, as mentioned in the first point, this figure is not a triangle, thus it is unable to be completed into a whole rectangle by doubling the shapes used in constructing the first figure.

Oh, I get it... problem solved, thank you very much... Chris Chai = Chai Chan Hoong? We lose contact after Form 3... 7 years already... Where are you now? Come add me on facebook... jackiechanhoileong@yahoo.com or give me your email, i will add you...

DeleteYeap, I go by that name now. Easier for people to remember. :)

DeleteThis comment has been removed by the author.

ReplyDeleteHi, Nice post! Would you please consider adding a link to my website on your page. Please email me back.

ReplyDeleteThanks!

Harry

harry.roger10@gmail.com

Give me your url. Is it this one: http://ithinkaboutmoneyallday.blogspot.com/ ?

Deletewow... your blog is cool Jackie.. keep posting, followback success #121 (Funny)

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