Regular/irregular regions | Year 5

01 / LEARN

The idea, step by step

Area measures a covering

Area tells us how much flat surface a region covers. Equal square units let us compare regions fairly. A square with side 1 cm has area 1 square centimetre, written cm².

For a rectangle of equal squares, count the squares in one row and multiply by the number of rows. A 4-by-3 array covers 12 unit squares. An irregular outline can also have a clear area.

Split or subtract carefully

Split an irregular region into rectangles, find each area and add. The pieces must not overlap, or some surface is counted twice. Draw the split lines when they help show your method.

You can also imagine a complete rectangle and subtract a missing part. Check that the smaller part is actually missing, and use the same units. Different correct methods should agree.

A common trap

Count the outline or add side lengths when asked for area.

Instead: Area counts square units covering the inside. Side lengths describe the boundary.

02 / WORKED EXAMPLES

See the thinking

Example 1

Count a stepped region

Find the area of the stepped region.

The top row contains 4 unit squares.
The next row contains 4 and the bottom row contains 2.
$4 + 4 + 2 = 10$ squares.
Each square has area 1 cm².

10 cm²

Example 2

Remove a corner

A 6 cm by 4 cm rectangle has a 2 cm by 2 cm corner removed. Find its remaining area.

Full rectangle: $6 \times 4 = 24$ cm².
Removed corner: $2 \times 2 = 4$ cm².
Remaining: $24 - 4 = 20$ cm².

20 cm²

Check your understanding

Rows of a shape contain 5, 5 and 3 unit squares. Find its area.

Show answer

13 square units

Add the non-overlapping rows: $5 + 5 + 3 = 13$ .

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Find the area of the rectangle.
2 marks
Find the area of this joined-square region.
2 marks
Two non-overlapping rectangles have areas 14 cm² and 9 cm². Find the combined area.
2 marks
A rectangle is 7 cm long and 5 cm wide. Find its area.
2 marks
A 5 cm by 4 cm rectangle has a 2 cm by 1 cm corner removed. Find the area left.
3 marks
A student splits a 6 cm by 3 cm rectangle into two pieces and says their areas total 21 cm². Explain why this cannot be right.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Find the area of the rectangle.
2 marks
There are 4 squares in each of 3 rows.
$4 \times 3 = 12$ cm².
12 cm²
Find the area of this joined-square region.
2 marks
Rows contain 5, 3 and 3 squares.
$5 + 3 + 3 = 11$ cm².
11 cm²
Two non-overlapping rectangles have areas 14 cm² and 9 cm². Find the combined area.
2 marks
$14 + 9 = 23$ cm².
23 cm²
A rectangle is 7 cm long and 5 cm wide. Find its area.
2 marks
$7 \times 5 = 35$ cm².
35 cm²
A 5 cm by 4 cm rectangle has a 2 cm by 1 cm corner removed. Find the area left.
3 marks
Full area: $5 \times 4 = 20$ cm².
Removed area: $2 \times 1 = 2$ cm².
$20 - 2 = 18$ cm².
18 cm²
A student splits a 6 cm by 3 cm rectangle into two pieces and says their areas total 21 cm². Explain why this cannot be right.
3 marks
$6 \times 3 = 18$ cm².
Splitting does not change the covered surface.
The original area is 18 cm², so a correct split must also total 18 cm². The student may have overlapped or miscalculated pieces.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics 2026

Units/precision; regular/irregular regions; boundary and area problems.

Official curriculum source ↗

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