The idea, step by step
Equal units cover fairly
To measure area, cover the whole region with equal square units. The units must meet without gaps and must not overlap. If one region is measured with large squares and another with tiny squares, their counts cannot be compared directly.
Whole and partial squares
Count complete squares first. Two half-squares can make one whole square. On an irregular boundary, pair parts that look close to a whole square and state that the result is an estimate. For a grid rectangle, equal rows give a quick way to count every square.
A common trap
Counting every touched square as a full square.
Instead: A touched square may only be partly covered. Combine parts and say when the answer is an estimate.
See the thinking
Equal rows
A rectangle covers 5 squares in each of 2 rows. Find its area.
- Count the first row: 5 square units.
- The second row also has 5.
- 5 + 5 = 10 square units.
Putting halves together
A region covers 6 whole grid squares and 4 half-squares. Find its area.
- Pair the 4 halves to make 2 whole squares.
- Add 6 + 2 = 8 square units.
Check your understanding
What area is covered by 3 whole squares and 2 half-squares?
Show answer
4 square units.
Two halves make 1 whole, so 3 + 1 = 4.
Your turn
6 questions · 8 marks · Work at your own pace.
Read the questions online
- A fully shaded grid has 4 columns and 3 rows. Find the area.1 mark
- Find the shaded area on the supplied grid.1 mark
- A region covers 7 whole squares and 2 half-squares. Find its area.1 mark
- A region covers 4 whole squares and 6 half-squares. Find its area.1 mark
- Why must square units not overlap when measuring area?2 marks
- A curved region covers 9 whole squares and several pieces that together look like about 3 whole squares. Estimate its area.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A fully shaded grid has 4 columns and 3 rows. Find the area.1 mark
4 + 4 + 4 = 12 square units.
12 square units. - Find the shaded area on the supplied grid.1 mark
Count the five shaded unit squares.
5 square units. - A region covers 7 whole squares and 2 half-squares. Find its area.1 mark
The two halves make 1 whole: 7 + 1 = 8.
8 square units. - A region covers 4 whole squares and 6 half-squares. Find its area.1 mark
Six halves make 3 wholes: 4 + 3 = 7.
7 square units. - Why must square units not overlap when measuring area?2 marks
Each part of the region should be counted once.
An overlap would count part of the region more than once. - A curved region covers 9 whole squares and several pieces that together look like about 3 whole squares. Estimate its area.2 marks
9 whole squares + about 3 from pieces gives about 12.
About 12 square 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 ↗