Monday, 10 September 2012

The Difference Between Area and Perimetre

....and how to avoid confusion

We've been exploring the area of 2D shapes and I have been postponing the introduction of the concept of "perimeter". Seems just about every text book you open introduces area and perimeter at the same time and from my experience this often leads to confusion for the kids.

So I've been putting it off until this morning.

And surprise, surprise, when I started talking about perimeter - we had confusion. It was limited, thankfully, to a few students only, probably because we had done so much focus on "area" that they already had that concept covered.

But it made me think, what would the kids say? How would they explain the difference between area and perimeter? And what suggestions would they have to help avoid any confusion?

The Difference Between Area and Perimeter According to the Kids...

  • Area is the stuff inside. Perimeter is the outside line.
  • Area is the whole thing and perimeter is just the outside.
  • Area is counting the shape inside.
  • Perimeter is the lines of the shape added together.
  • Perimeter is the length around the shape, area is the space in the shape.
  • One you multiply and the other you add.
  • Perimeter is the outline.

And Some Strategies to Avoid Confusion...

  • Area is 2D and perimeter is length which is only 1D.
  • Perimeter has "meter" in it so it is length.
  • Use the "Kruger Method" - named after one student who decided to trace around the outside of a shape using a coloured marker pen so he could add up the perimeter as he went. 
  • Use the "Walker Method" - named after the student who divided his shapes up into square centimetres with a ruler and then put a coloured dot in each as he was adding up the area
  • "For fun, my mum and I say 'peri' means outside. So perimeter means length around the outside." - which is pretty good. Other meanings include "about", "around", "near", "surrounding".

The Kruger Method

The Walker Method

So what?

My advice would be, don't introduce area and perimeter at the same time.

Choose one of them and get it consolidated before you move on to the other one.

Use really simple ideas, like the Kruger Method and the Walker Method, when working with these concepts.

Ask the kids to tell you what their ideas are and what they are doing to tell the difference - it offers a great insight into their brains and how what features they are focusing on.


  1. Now give them this; find the perimeter and area of a rectangle with very thick lines. Where does the area stop and the perimeter begin?

  2. So we considered a shape with really thick edges for homework and decided (eventually):
    1. the perimeter isn't part of the shape
    2. the perimeter has no thickness the thickness of the border doesn't matter - you measure the inside of the thick line to get the perimeter (some kids did take some convincing)
    BUT in the real world (not the world of 2D shapes) we can measure the outside of the line - like in a house where the area of the house includes the thickness of the walls.
    An interesting conversation!

  3. Someone else this week posted on a similar topic about introducing concepts at different times. I agree with you that they should not be introduced at the same time as that leads to confusion. Thanks for sharing your student insights!


Any comments you would like to make?