Expert: Josh - 10/5/2005

Question
My son has brought a chart home about perimeter, it is broken into 3 columns
first column shape #, second column is process (N), and third column is the actual perimeter.

1 - N - 4
2 - N - 6
3 - N - 8
4 - N - 10
5 - N - 12
6 - N - 14

They are pasting the 1 x 1 squares to the left of this with of course the 1 applying to 1 square used.  I think I am making a mountain out of a mole hill and can't for the life of me fiqure out how the N is used.  I understand perimeter but I can't figure out what this teacher wants.

Answer
Hi Cheryl,

This is what I think, let me try to explain this with the symbol "L". Can you pretend that "L" is one of the 1-by-1 square units? I can't find a box in my character set as I type.

Okay, when the order N=1, we have 1 square unit "L". Since a square has four edges that are identical in length, the perimeter of a single square unit is 1+1+1+1=4 units.

When the order N=2, we form a block by placing two square units next to each other, like "LL".
The height hasn't change, still measuring one unit.
But the width has doubled, since it now spans across two square units.
So, the perimeter may be informally stated as the sum of the "left","top","right" and "bottom" edges,
i.e., 1+2+1+2=6.

Continuing with this block building pattern, when N=3, we join together three square units to produce "LLL".
Using the same conventions, the perimeter is given by 1+3+1+3=8 and so forth.

I hope you can make sense of this and explain it to your son.

Cheers.