Expert: Azeem Hussain - 6/16/2009

Question
QUESTION: Hello Azeem,

Why is perimeter measured in units and area is measured in square units? Please give examples to clarify your explanation. Additionally, why would we measure volume in cubic units?

Thanks in advance.

ANSWER: Hi Dwayne,

When you're measuring perimeter you are only dealing with one dimension.  If I asked you to find the perimeter of a square whose side measures 2 m, you would instinctively say it was 8 m.  You would probably show your work like this:
p=4(2)
p=8 m

Now do it, but carry the units m throughout the calculation.
p=4(2 m)
p=8 m

In one dimension, this is trivial.  Let's try in two.  Find the square's area.  Once again carry the units.
A=(2 m)(2 m)
A=4 m²

When multiplying meter by meter (m times m), you get m².  The same principle applies to volume.
v=(2 m)(2 m)(2 m)
v=8 m^3

Thanks for asking,
Azeem

---------- FOLLOW-UP ----------

QUESTION: Thanks Azeem. Just to follow-up on the last part of my question - why would we measure volume in cubic units?

Answer
Dwayne,

Reread the last part of my answer.  It's essentially the same as with area, but in three dimensions.  Volume would be found by, say, multiplying length by width by height.  If these are all measured in meters, then you have (m)(m)(m)=m^3.

Hope this helps,
Azeem