View Full Version : A Frustrating Puzzle

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.

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.

;)