Pentominoes (area and perimeter)
Stage 2 and 3 – A thinking mathematically targeted teaching opportunity focussed on investigating the perimeter of rectangles with equivalent areas.
Inspired by MathXplosion – Area vs perimeter
Syllabus outcomes and content descriptors from Mathematics K-10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2021
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 we 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.
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.
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.
They look pretty different... and they still have the same area!
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.