Boundary and area problems | Year 5

01 / LEARN

The idea, step by step

Boundary or inside?

Perimeter is the total length around the outside of a flat shape. A fence, frame or edge strip usually needs perimeter. Area measures the surface inside. Paint, lawn and covering tiles usually need area. Read what the material must cover before calculating.

Opposite sides of a rectangle are equal. Add all four sides, or double the sum of length and width. Use length units such as centimetres for perimeter and square units such as cm² for area.

Finish the practical answer

A boundary problem may include a gate opening. Find the full perimeter first and subtract the opening only if it does not need fencing. A covering problem may have a hole or border, so count only the surface actually covered.

Changing the shape of a rectangle can change its area even when its perimeter stays equal. A long thin rectangle and a square may use equal edging but enclose different surfaces. Use both calculations to support a comparison.

A common trap

Assume an equal perimeter means an equal area.

Instead: Check each measure separately. The boundary length does not uniquely determine the enclosed area.

02 / WORKED EXAMPLES

See the thinking

Example 1

Fence with a gate

An 8 m by 5 m rectangular garden has a 2 m gate opening that needs no fence. Find the fence length.

Full perimeter: $8 + 5 + 8 + 5 = 26$ m.
Subtract the gate: $26 - 2 = 24$ m.
The gate is a boundary length, not an area.

24 m

Example 2

Same perimeter, different area

Compare a square with side 4 cm and a 6 cm by 2 cm rectangle.

Square: perimeter $4 + 4 + 4 + 4 = 16$ cm; area $4 \times 4 = 16$ cm².
Rectangle: perimeter $6 + 2 + 6 + 2 = 16$ cm; area $6 \times 2 = 12$ cm².
The perimeters match but the areas differ by $16 - 12 = 4$ cm².

Both perimeters are 16 cm; the square has 4 cm² more area.

Check your understanding

A photo is 9 cm by 6 cm. How much edging goes once around it?

Show answer

30 cm

Edging follows the perimeter: $9 + 6 + 9 + 6 = 30$ cm.

03 / WORKSHEET

Your turn

6 questions · 15 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Find the perimeter of a 7 cm by 3 cm rectangle.
2 marks
Find the perimeter of a square with side 6 m.
2 marks
A rectangle has perimeter 24 cm and width 4 cm. Find its length.
3 marks
A 10 m by 4 m garden has a 3 m opening. Find the fencing length.
2 marks
Choose area or perimeter for each task.
2 marks
1. (a)
  Carpet to cover a room.
  1 mark
2. (b)
  Ribbon around a card.
  1 mark
Compare a 5 cm by 5 cm square and a 7 cm by 3 cm rectangle. Check their perimeters and compare their areas.
4 marks

Read the worked solutions

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

Find the perimeter of a 7 cm by 3 cm rectangle.
2 marks
$7 + 3 + 7 + 3 = 20$ cm.
20 cm
Find the perimeter of a square with side 6 m.
2 marks
$4 \times 6 = 24$ m.
24 m
A rectangle has perimeter 24 cm and width 4 cm. Find its length.
3 marks
Two widths: $2 \times 4 = 8$ cm.
Two lengths: $24 - 8 = 16$ cm.
One length: $16 \div 2 = 8$ cm.
8 cm
A 10 m by 4 m garden has a 3 m opening. Find the fencing length.
2 marks
Perimeter: $10 + 4 + 10 + 4 = 28$ m.
$28 - 3 = 25$ m.
25 m
Choose area or perimeter for each task.
2 marks
Carpet covers an inside surface.
Ribbon follows an outside boundary.
1. (a)
  Carpet to cover a room.
  1 mark
  Carpet covers the inside surface.
  Area
2. (b)
  Ribbon around a card.
  1 mark
  Ribbon follows the outside boundary.
  Perimeter
Carpet needs area; ribbon around a card needs perimeter.
Compare a 5 cm by 5 cm square and a 7 cm by 3 cm rectangle. Check their perimeters and compare their areas.
4 marks
Square: perimeter $4 \times 5 = 20$ cm; area $5 \times 5 = 25$ cm².
Rectangle: perimeter $7 + 3 + 7 + 3 = 20$ cm; area $7 \times 3 = 21$ cm².
Both perimeters are 20 cm. The areas are 25 cm² and 21 cm², so the square has 4 cm² more area.

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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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