Area vs perimeter

Collect resources

You will need:

  • something to write on

  • something to write with

  • a set of pentominoes (see the pentominoes task to learn how to create your own)

Before you begin

In the pentominoes task we challenged you to create two different rectangles using all 12 pentomino pieces. Looking at this challenge has reminded us that numbers can have the same value but look quite different, and has made us wonder how creating different rectangles will affect the area and perimeter of these shapes.

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!

For more information on area and perimeter, you might like to check check out MathXplosion –area vs perimeter.

Instructions

  • What other rectangles can you make that have an area of 60 squares?

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

  • Find as many rectangles as possible and record their perimeter and area.