Saturday, December 27, 2008

Can someone explain this to me?


This "illusion" was on a cereal box that I was looking at this morning and I can't figure it out. It's really bugging me. Both triangles were created with the exact same four shapes. In the first one, all four shapes take up the entire area of the larger triangle. In the second, the shapes are rearranged to create the exact same size larger triangle, but this time there is a one-unit square missing. How is that possible?

(Edit: Actually, I think I figured it out....)

2 Comments:

At 11:09 PM, Anonymous Meg said...

I'm lost... feel free to enlighten us when you figure it out!

:D
Meg

 
At 6:46 PM, Blogger Andy Efting said...

To begin with, the overall large triangle has a base of 13 units and a height of 5 units. Thus the area = 1/2(BxH) = 1/2(13*5) = 32.5.

Now, calculate the areas of the individual objects given what appears to be their dimensions, i.e., that the purple triangle has a base of 8 units and a height of 3. The cyan triangle has a height of 2 units and a base of 5. The l-shaped figures are 5 units long and either 2 or 3 unit squares attached. Do the math and you will find out that it doesn't equal 32.5.

The problem is that objects look like more of a perfect fit than they really are. The devil is in the details, as it were.

 

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