Understand the idea.
Use the same measure
First decide what to compare. For area, cover each shape with the same-sized square units. For perimeter, measure each outside boundary using the same length unit. A shape that looks longer may not cover more space.
Keep the two comparisons separate. Count or calculate the areas to compare surface coverage; add the outside side lengths to compare boundary lengths. One comparison cannot replace the other.
Same area, different boundary
Rearranging six equal tiles into a 1 by 6 strip or a 2 by 3 rectangle keeps the area at 6 square units. The tiles are the same and none have been added or removed.
The arrangement changes which edges are exposed. The strip has perimeter units; the compact rectangle has perimeter units. Equal areas can therefore have different perimeters.
See the method in action.
Two rectangles
Compare a 4 by 2 rectangle and a 3 by 3 square using unit squares.
Worked solution
- 1
Count the 4 by 2 rectangle.
There are two rows, each containing four unit squares.
- 2
Count the 3 by 3 square.
There are three rows, each containing three of the same unit squares.
- 3
Find the area difference.
The 3 by 3 square covers one more unit square than the rectangle.
The 3 by 3 square has 1 more square unit of area.
An equal perimeter
A 5 cm by 1 cm rectangle and a 4 cm by 2 cm rectangle are compared.
Worked solution
- 1
Find the first perimeter.
The 5 cm by 1 cm rectangle has two sides of each length.
- 2
Find the second perimeter.
The 4 cm by 2 cm rectangle also needs all four sides counted.
- 3
Find the first area.
One row of five 1-centimetre squares covers the first rectangle.
- 4
Find the second area and compare.
Two rows of four squares cover the second rectangle: the perimeters match, but the areas are 5 and 8 square centimetres.
Both perimeters are 12 cm; their areas are different.
Try it yourself.
Check your understanding
Do a 1 by 4 strip and a 2 by 2 square have the same area?
Show answer & reasoning
Yes: 4 square units each.
Yes. The strip contains unit squares and the square contains unit squares. Their areas match because the same-sized squares are counted, even though the boundaries differ.
Keep practising
6 worksheet questions · 8 marks
Read the questions online
- Which has more area: 2 rows of 5 unit squares or 3 rows of 3?1 mark
- Compare the areas of a 1 by 8 strip and a 2 by 4 rectangle.1 mark
- Find the perimeter of a 1 cm by 8 cm rectangle.1 mark
- Find the perimeter of a 2 cm by 4 cm rectangle.1 mark
- Two gardens both have 16 m of fence. Must they have the same area? Explain.2 marks
- Arrange 6 unit squares into two different rectangles. Compare their boundaries.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Which has more area: 2 rows of 5 unit squares or 3 rows of 3?1 mark
10 is greater than 9.
2 rows of 5: 10 square units, which is 1 more. - Compare the areas of a 1 by 8 strip and a 2 by 4 rectangle.1 mark
Each arrangement contains eight unit squares.
Both have area 8 square units. - Find the perimeter of a 1 cm by 8 cm rectangle.1 mark
cm.
18 cm. - Find the perimeter of a 2 cm by 4 cm rectangle.1 mark
cm.
12 cm. - Two gardens both have 16 m of fence. Must they have the same area? Explain.2 marks
Equal outside distance does not fix the amount of inside space.
No. For example, 1 m by 7 m and 4 m by 4 m have perimeter 16 m but areas 7 and 16 square metres. - Arrange 6 unit squares into two different rectangles. Compare their boundaries.2 marks
Both cover 6 square units.
Count the outside unit edges of each arrangement.
1 by 6 has perimeter 14 units; 2 by 3 has perimeter 10 units.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Boundary/interior; measuring perimeter; covering/counting/estimating area; comparing shapes.
Official curriculum source ↗