Deriving rectangle area | Year 6

01 / LEARN

Understand the idea.

Cover a surface with square units

Area counts the equal square units needed to cover a surface, with no gaps or overlaps. A square measuring $1 cm$ along each side is one square centimetre, written $1 {cm}^{2}$ .

In the diagram, each row contains $4$ unit squares and there are $3$ rows. Multiplication counts every square once: $4 \times 3 = 12$ . This row-and-column structure explains why a rectangle has area equal to length times width.

Use length times width

Write $A = l \times w$ , where $A$ is area, $l$ is length and $w$ is width. Express both side lengths in the same unit before multiplying. Centimetres times centimetres gives square centimetres; metres times metres gives square metres.

Perimeter measures the distance around the boundary, so it uses ordinary length units. Decide whether the task asks for covering the inside or measuring the edge before choosing multiplication or addition. Equal areas do not guarantee equal perimeters.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example 1

Find the area of a rectangle 8 centimetres long and 5 centimetres wide.

Worked solution

1
Choose the rectangle area formula.
$A = l \times w$
The length gives the number of unit squares in each row and the width gives the number of rows.
2
Substitute the two side lengths.
$A = 8 \times 5$
Both dimensions are already measured in centimetres.
3
Calculate the covered surface.
$A = 40 {cm}^{2}$
There are five rows of eight one-square-centimetre units.

Answer

40 square centimetres.

EXAMPLE 02

Worked example 2

A rectangle is 2 metres long and 50 centimetres wide. Find its area in square centimetres.

Worked solution

1
Convert the length to centimetres.
$2 m = 2 \times 100 cm = 200 cm$
The required area unit is square centimetres, so both side measurements must use centimetres.
2
Multiply the matching-unit side lengths.
$A = 200 \times 50$
A rectangle contains length times width square units.
3
State the area in square units.
$A = 10 000 {cm}^{2}$
The multiplication counts one-centimetre squares rather than centimetres of boundary.

Answer

10,000 square centimetres.

03 / YOUR TURN

Try it yourself.

Check your understanding

A rectangle has 6 rows of 9 unit squares. What is its area?

Show answer & reasoning

54 square units.

Each of the $6$ rows contains $9$ unit squares, so $6 \times 9 = 54$ . The area is $54$ square units.

Keep practising

6 worksheet questions · 8 marks

Open worksheet Worked solutions

Read the questions online

Find the area of a 7 cm by 4 cm rectangle.
1 mark
Find the area of a 12 m by 3 m rectangle.
1 mark
Find the area of a square with side 9 cm.
1 mark
A grid has 5 rows and 8 columns of one-centimetre squares. Find its area.
1 mark
A rectangle is 1 m long and 30 cm wide. Find its area in square centimetres.
2 marks
A 6 cm by 4 cm rectangle has perimeter 20 cm. Is its area also 20 square centimetres? Explain.
2 marks

Read the worked solutions

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

Find the area of a 7 cm by 4 cm rectangle.
1 mark
$7 \times 4 = 28$ .
28 square centimetres.
Find the area of a 12 m by 3 m rectangle.
1 mark
$12 \times 3 = 36$ .
36 square metres.
Find the area of a square with side 9 cm.
1 mark
$9 \times 9 = 81$ .
81 square centimetres.
A grid has 5 rows and 8 columns of one-centimetre squares. Find its area.
1 mark
$5 \times 8 = 40$ .
40 square centimetres.
A rectangle is 1 m long and 30 cm wide. Find its area in square centimetres.
2 marks
$1 m = 100 cm$ ; $100 \times 30 = 3, 000$ .
3,000 square centimetres.
A 6 cm by 4 cm rectangle has perimeter 20 cm. Is its area also 20 square centimetres? Explain.
2 marks
$Area = 6 \times 4 = 24$ ; $perimeter = 6 + 4 + 6 + 4 = 20$ .
No. Its area is 24 square centimetres.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Decimal metric conversions; deriving rectangle area; missing dimensions; practical measurement.

Official curriculum source ↗

In this lesson

Understand the idea.

Cover a surface with square units

Use length times width

See the method in action.

Worked example 1

Choose the rectangle area formula.

Substitute the two side lengths.

Calculate the covered surface.

Worked example 2

Convert the length to centimetres.

Multiply the matching-unit side lengths.

State the area in square units.

Try it yourself.

Check your understanding

Keep practising