Area vs perimeter

Before you begin

Get your work from the Pentominoes activity. In Pentominoes you were challenged to create some rectangles with your pentominoes. If you didn't work them out yet, there are some examples below.

Collect resources

You will need:

  • a pencil

  • student workbook.

Remember our pentomino challenge?

We asked you to make some rectangles – one with the smallest possible perimeter and one with the largest possible perimeter. Looking at numbers in different ways has reminded us of this challenge! We’re realising that numbers can have the same value but look quite different. Look at these two rectangles:

Here’s one rectangle I could have made using all 12 pentomino pieces.

The rectangle is made of different shaped pentominos. It is 6 squares high and 10 squares long.

It forms a rectangle with boundaries of 6+10+6+10 making the perimeter 32 squares long. The area inside the rectangle is 60 squares.

Here’s a different rectangle I could have made using all 12 pentomino pieces.

The rectangle is made of different shaped pentominos. It is 3 squares high and 20 squares long.

It forms a rectangle with boundaries of 3+20+3+20 making the perimeter 46 squares long. The area inside the rectangle is 60 squares.

My conclusion

They look pretty different...and they still have the same area!

Instructions

  • View episode MathXplosion –area vs perimeter on ABC splash.

  • What rectangles can you make that have an area of 24 squares?

  • Try to find 2 other rectangles and record their perimeter and area.

  • You can use your pentomino pieces to help you, or some grid paper.