IQ test [Updated, May 2012]

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?