The idea, step by step
Use the same measure
Compare areas by covering both regions with the same square unit. Compare perimeters by measuring both outside boundaries with the same length unit. A long-looking shape does not necessarily cover more space than a compact one. Decide which measure the question asks for before comparing.
Same area, different boundary
Six unit squares can form a 1 by 6 strip or a 2 by 3 rectangle. Both cover 6 square units. Their perimeters differ: the strip is 14 units around, while the rectangle is 10 units around. Rearranging equal tiles can change the boundary without changing how many tiles there are.
A common trap
A larger perimeter always means a larger area.
Instead: Perimeter and area measure different features. Calculate or count each one.
See the thinking
Two rectangles
Compare a 4 by 2 rectangle and a 3 by 3 square using unit squares.
- The rectangle covers 4 + 4 = 8 square units.
- The square covers 3 + 3 + 3 = 9 square units.
- The square has the larger area by 1 square unit.
An equal perimeter
A 5 cm by 1 cm rectangle and a 4 cm by 2 cm rectangle are compared.
- First boundary: 5 + 1 + 5 + 1 = 12 cm.
- Second boundary: 4 + 2 + 4 + 2 = 12 cm.
- Their areas are 5 and 8 square centimetres, so equal perimeter does not mean equal area.
Check your understanding
Do a 1 by 4 strip and a 2 by 2 square have the same area?
Show answer
Yes: 4 square units each.
Both contain four equal unit squares, even though their boundaries differ.
Your turn
6 questions · 8 marks · Work at your own pace.
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
1 + 8 + 1 + 8 = 18 cm.
18 cm. - Find the perimeter of a 2 cm by 4 cm rectangle.1 mark
2 + 4 + 2 + 4 = 12 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 ↗