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jfrenaye
07-26-2005, 04:36 PM
I have tried to figure this out for years. I have had math teachers bail out on me. I do not believe the internet solutions as they all seem so miniscule as to make a difference. I have cut this out from graph paper and I still have no clue.....anyone?

http://www.simeonmagic.com/images/Triangle.gif

mishka422
07-27-2005, 10:49 AM
It's not really a matter of the blank space. It's not really blank. There just is no color in it because of the way the patterned blocks have been moved. The entire figure takes up the same amount of space regardless of the fact that the one block has no color.

jfrenaye
07-27-2005, 10:54 AM
I don't buy that mishka--

The outer dimensions of the triangle are the same in both drawings. THe area of the triangle is B*H*.5 or B*H/2. The area of the entire shape is the consistent. The area of each individual shape is also consistent.

Yet when rearranged, the colored area is 1 unit shy.

Cheri
07-27-2005, 01:50 PM
Sorry John,
I have to agree with Mishka!! No math is involved!!! You still are covering the same space but one square is blank. It is just the way it is arranged. Make sense to me. :D
Cheri
the Math Major..... "ha ha!!!" What am I doing in the travel business?? :D

mishka422
07-27-2005, 01:51 PM
You're overthinking it! :) I don't think it is truly a math problem, it is simply an exercise of how your mind works. You're is extremely analytical and mine is more toward the creative.

Cheri
07-27-2005, 01:53 PM
I must be creative too!!!
Cheri :D

mishka422
07-27-2005, 01:56 PM
It's like a jigsaw puzzle. They still fit in the same square but if you move the pieces around they will not fit. Same thing.

tdew
07-27-2005, 02:13 PM
John,

I think if you look closely, you'll see that the bottom illustration covers more of the white space at the top of the red triangle, so that makes room for the empty square on the bottom.

Terry

jfrenaye
07-27-2005, 03:38 PM
The area of a triangle is calculated the same way. Both are right angle triangles and both have the same area (outer perimeter of the larger shape)

Still not getting it

Stwtravel
07-27-2005, 10:40 PM
Originally posted by jfrenaye@Jul 27 2005, 03:38 PM
The area of a triangle is calculated the same way. Both are right angle triangles and both have the same area (outer perimeter of the larger shape)

Still not getting it
5720

Let me give this a shot.

What we have here is an optical illusion. Putting all the shapes together does not make a right triangle.

Area of:
red triangle - 12 squares
green triangle - 5 squares
orange block - 7 squares
green block - 8 squares

Total area of shapes - 32 squares
area of "large triangle" would be 5*13/2 or 32.5 squares

While it is close the blocks do not form a triangle.

jfrenaye
07-28-2005, 06:36 AM
This is my last post on this but Sally--isn't the area of the pieces the same in both illustrations? The area or the larger triangles is also the same in both illustrations.

I have cut this out wtih graph papre and tried it to prove it and I am still not getting it.

;)