Perimeter and composite area | Year 11

01 / LEARN

The idea, step by step

Understand the idea

Perimeter measures the outside boundary, while area measures the enclosed region. A line used to split a composite shape is not part of its outside boundary. Label all dimensions before choosing formulas.

An L-shaped region can be split into non-overlapping rectangles or found by removing a corner from a bounding rectangle. The two methods provide a useful independent check.

Choose and apply a method

Keep length units consistent. Use length units for perimeter and square units for area. A triangular height must be perpendicular to its base; a sloping side is not automatically the height.

Show the decomposition and explain missing dimensions. If a corner has been removed, the result must be smaller than the bounding rectangle. Curved boundaries require arc length, not the diameter.

A_{rectangle} = l w, A_{triangle} = \frac{1}{2} b h

A common trap

Adding every line in a decomposed diagram to obtain perimeter.

Instead: Only the outside boundary counts; internal construction lines do not.

02 / WORKED EXAMPLES

See the thinking

Example 1

Remove a corner

A 12 m by 6 m rectangle has a 4 m by 3 m corner removed. Find remaining area.

Bounding rectangle area $= 12 \times 6 = 72$ .
Removed corner area $= 4 \times 3 = 12$ .
Remaining area $= 72 - 12 = 60$ m $2$ .

60 m

2

Example 2

Leave an entrance

A garden is 8 m long and 5 m wide. A 2 m entrance is left unfenced. Find required fencing.

Full perimeter $= 2 (8 + 5) = 26$ m.
Subtract entrance: $26 - 2 = 24$ m.

24 m.

Check your understanding

A 10 cm by 7 cm rectangle has a 3 cm by 2 cm corner removed. Find area.

Show answer

64 cm $2$ .

$10 \times 7 - 3 \times 2 = 70 - 6 = 64$ .

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Find perimeter and area of a 9 m by 4 m rectangle.
2 marks
A 15 m by 8 m rectangle has a 5 m by 3 m corner removed. Find area.
2 marks
A triangle has base 14 cm and perpendicular height 9 cm. Find area.
2 marks
Find perimeter of the illustrated L-shape.
3 marks
A 6 m by 4 m room has a 2 m by 1 m alcove added outside a wall, with no overlap. Find floor area.
2 marks
A circular pond has radius 3 m. Find circumference to 2 decimal places.
2 marks

Read the worked solutions

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

Find perimeter and area of a 9 m by 4 m rectangle.
2 marks
$P = 2 (9 + 4) = 26$ .
$A = 9 \times 4 = 36$ .
26 m; 36 m $2$ .
A 15 m by 8 m rectangle has a 5 m by 3 m corner removed. Find area.
2 marks
$15 \times 8 - 5 \times 3 = 120 - 15 = 105$ .
105 m $2$ .
A triangle has base 14 cm and perpendicular height 9 cm. Find area.
2 marks
$A = \frac{1}{2} \times 14 \times 9 = 63$ .
63 cm $2$ .
Find perimeter of the illustrated L-shape.
3 marks
The removed outer lengths are replaced by equally long notch edges.
Perimeter remains $2 (12 + 6) = 36$ m.
36 m.
A 6 m by 4 m room has a 2 m by 1 m alcove added outside a wall, with no overlap. Find floor area.
2 marks
$6 \times 4 + 2 \times 1 = 24 + 2 = 26$ .
26 m $2$ .
A circular pond has radius 3 m. Find circumference to 2 decimal places.
2 marks
$C = 2 π r = 6 π$ .
$6 π \approx 18.85$ m.
18.85 m.

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Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics measurement skills and applications; original explanatory lessons and papers.

Official curriculum source ↗

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