Finding missing rectangle dimensions | Year 6

01 / LEARN

Understand the idea.

Undo the multiplication

Rectangle area is found by multiplying two perpendicular side lengths. If one side is missing, ask what number multiplied by the known side gives the area. Division reverses that multiplication: $missing side = area \div known side$ .

For an area of $30 {cm}^{2}$ and a width of $5 cm$ , the length is $30 \div 5 = 6 cm$ . The answer uses a length unit because it measures one side, rather than the whole surface.

Check more than the number

Check a found side by multiplying it by the known side. The product must recover the original area, with the correct square unit. This catches both a wrong operation and many calculation mistakes.

Area on its own does not select just one rectangle. Both $6 cm \times 4 cm$ and $8 cm \times 3 cm$ give $24 {cm}^{2}$ . Knowing one side supplies the extra information needed to find the other.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example 1

A rectangle has area 56 square centimetres and width 7 centimetres. Find its length.

Worked solution

1
Write the area relationship.
$l \times 7 = 56$
The unknown length multiplied by the known width must equal the area.
2
Divide by the known width.
$l = 56 \div 7 = 8 cm$
Division undoes multiplication by seven.
3
Check using the area formula.
$8 \times 7 = 56 {cm}^{2}$
The calculated length and the given width reproduce the stated area.

Answer

8 cm.

EXAMPLE 02

Worked example 2

A rectangular garden has area 72 square metres. One side is 12 metres. Find the other side and the perimeter.

Worked solution

1
Find the missing side from the area.
$other side = 72 \div 12 = 6 m$
The two side lengths multiply to the area of the garden.
2
Check the pair of side lengths.
$12 \times 6 = 72 m^{2}$
The dimensions match the given area.
3
Add the four boundary lengths.
$P = 12 + 6 + 12 + 6 = 36 m$
Opposite sides of a rectangle are equal, and perimeter counts all four sides.

Answer

Other side 6 m; perimeter 36 m.

03 / YOUR TURN

Try it yourself.

Check your understanding

Area is 45 square metres and one side is 9 metres. Find the other side.

Show answer & reasoning

5 m.

The other side is $45 \div 9 = 5 m$ . Checking gives $9 \times 5 = 45 m^{2}$ , the required area.

Keep practising

6 worksheet questions · 9 marks

Open worksheet Worked solutions

Read the questions online

A rectangle has area 24 square centimetres and width 4 cm. Find its length.
1 mark
A rectangle has area 63 square metres and length 9 m. Find its width.
1 mark
A rectangle has area 100 square centimetres and width 5 cm. Find its length.
1 mark
Give two different whole-number side pairs for a rectangle of area 36 square centimetres.
2 marks
A 48-square-metre garden has width 6 m. Find its length and perimeter.
2 marks
A rectangle has area 42 square centimetres and one side of 7 cm. A learner calculates $42 - 7$ to find the other side. Explain the error and find the correct side length.
2 marks

Read the worked solutions

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

A rectangle has area 24 square centimetres and width 4 cm. Find its length.
1 mark
$24 \div 4 = 6$ .
6 cm.
A rectangle has area 63 square metres and length 9 m. Find its width.
1 mark
$63 \div 9 = 7$ .
7 m.
A rectangle has area 100 square centimetres and width 5 cm. Find its length.
1 mark
$100 \div 5 = 20$ .
20 cm.
Give two different whole-number side pairs for a rectangle of area 36 square centimetres.
2 marks
Both products equal 36. Other valid pairs are acceptable.
For example, 9 cm by 4 cm and 12 cm by 3 cm.
A 48-square-metre garden has width 6 m. Find its length and perimeter.
2 marks
$48 \div 6 = 8$ ; $8 + 6 + 8 + 6 = 28$ .
Length 8 m; perimeter 28 m.
A rectangle has area 42 square centimetres and one side of 7 cm. A learner calculates $42 - 7$ to find the other side. Explain the error and find the correct side length.
2 marks
The area formula multiplies the side lengths, so division, not subtraction, undoes it.
Divide 42 by 7 to get 6 cm.

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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.

Undo the multiplication

Check more than the number

See the method in action.

Worked example 1

Write the area relationship.

Divide by the known width.

Check using the area formula.

Worked example 2

Find the missing side from the area.

Check the pair of side lengths.

Add the four boundary lengths.

Try it yourself.

Check your understanding

Keep practising