how does this triangle puzzle work?

Factual Questions
1

I’ve tried analyzing this and can’t figure it out:

http://www.simeonmagic.com/triangle/triangle1.htm
(sorry, I don’t know how to link)

The triangle on a whole is 32.5 units squared.

One of the internal trinagles is 5 units squared and the other is 12 units squared.

So why does the remaining square equal either 15 or 16 units squared depending on where the internal triangles are placed.

Adding the sum of the parts one way equals 32 and the other 33.
Why do the sum of the parts not equal 32.5??

2

There have been many threads about this. The lines are not perfectly straight, the figure is not drawn perfectly accurate (depending which version you look at), it’s off just enough to account for the difference.

3

This has come up quite a few times. Here’s just one:
http://boards.straightdope.com/sdmb/showthread.php?threadid=89065

4

The best answer from the other thread:

Actually, you are dealing with 1 four sided figure, and one 8 sided figure!

5

Sorry, but I have to nitpick. The slopes are actually

Red Triangle = 3 up by 8 over. Slope = 3/8 = .375

Green Triangle = 2 up by 5 over. Slope = 2/5 = .4

They are still different.

6

Did you know that the missing square costs exactly a dollar and sounds like a duck?

7

duck?

8

“Quack!”
<pause>
" … !"

<puzzled glances>

9

Is there an echo in here? :wink:

10

Furthermore, it smells of cat food and is the only square that cannot jump.

11

Hungry though I may be for knowledge, squares like this make me so angry and … and … I dunno: Something else.

12

Brilliant… Absolutely brilliant!

::applause::

13

Yeah, but where did the missing leprechaun go?

14

My friend has a square that he is worried might be smaller than average; what is the average size of a sqare?

15

Is the missing square large enough to hide the third -gry in?

16

All your square are belong to us.

17

When come back, bring square!

18

  1. This is just an optical illusion wherein the brain “fills in the blanks” and makes you see what truly is not there.

  2. A simple analytical look matching the intersections of the triangle legs to the background grid will reveal this.

  3. Hi Square!

19

Be honest, does the size of the square really matter?

20

This is actually an old mathematical debate.

The area of the triangle is actually 32.4999~. The difference between this value and the genuine value of exactly 32.5 is represented by the square seen in the bottom figure.

I hope this helps…