The idea, step by step
Perimeter is the distance around
Imagine walking once around the outside edge. Every boundary segment counts once. An internal line does not count unless the problem explicitly asks for that boundary too. Add lengths only after putting them in the same unit. A rectangle has two copies of its length and two copies of its width.
Missing edges and real boundaries
In an L-shaped rectilinear outline, horizontal steps together span the full width and vertical steps span the full height. Use subtraction to find an unlabelled section, then check that no edge has been counted twice. Draw and label a simple sketch before doing arithmetic.
A fence question may include a gate. First find the complete boundary, then subtract the opening. Area tells us how much ground is covered; perimeter tells us how much edging is needed. Those answers have different units.
A common trap
Multiplying length by width to find a perimeter.
Instead: Length × width measures the inside area. Trace and add the outer edges for perimeter.
See the thinking
A complete rectangular boundary
Find the perimeter of a rectangle 9 cm long and 4 cm wide.
- The four sides are 9, 4, 9 and 4 cm.
- Add them, or use 2(9 + 4).
Fence with an opening
A rectangular garden is 12 m by 7 m. A 2 m gate needs no fencing. How much fencing is needed?
- Complete perimeter = 2(12 + 7) = 38 m.
- Subtract the 2 m gate: 38 − 2 = 36 m.
Check your understanding
A square has side 6.5 cm. What is its perimeter?
Show answer
26 cm
Four equal sides give 4 × 6.5 = 26 cm.
Your turn
6 questions · 14 marks · Work at your own pace.
Read the questions online
- Find the perimeter of a rectangle 8 cm by 3 cm.2 marks
- A triangle has sides 5 cm, 7 cm and 9 cm. Find its perimeter.1 mark
- A rectangle has perimeter 30 m and length 9 m. Find its width.3 marks
- Find the perimeter of the L-shaped outline shown. The missing corner is 4 m wide and 3 m high.3 marks
- A 10 m by 6 m garden has a 1.5 m gate. Find the fencing length.2 marks
- Two rectangles each have area 24 cm². One is 6 cm by 4 cm; the other is 8 cm by 3 cm. Compare their perimeters.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find the perimeter of a rectangle 8 cm by 3 cm.2 marks
2(8 + 3) = 22 cm.
22 cm - A triangle has sides 5 cm, 7 cm and 9 cm. Find its perimeter.1 mark
5 + 7 + 9 = 21 cm.
21 cm - A rectangle has perimeter 30 m and length 9 m. Find its width.3 marks
The two long sides total 18 m.
The other two sides total 30 − 18 = 12 m.
Each width is 12 ÷ 2 = 6 m.
6 m - Find the perimeter of the L-shaped outline shown. The missing corner is 4 m wide and 3 m high.3 marks
Top short side = 9 − 4 = 5 m; right lower side = 7 − 3 = 4 m.
Boundary = 5 + 3 + 4 + 4 + 9 + 7.
Total = 32 m.
32 m - A 10 m by 6 m garden has a 1.5 m gate. Find the fencing length.2 marks
Complete perimeter = 2(10 + 6) = 32 m.
32 − 1.5 = 30.5 m.
30.5 m - Two rectangles each have area 24 cm². One is 6 cm by 4 cm; the other is 8 cm by 3 cm. Compare their perimeters.3 marks
First perimeter: 2(6 + 4) = 20 cm.
Second perimeter: 2(8 + 3) = 22 cm.
The different side lengths change the boundary length.
20 cm and 22 cm; equal area does not imply equal perimeter.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 7 measurement and spatial representation: areas of triangles/parallelograms, prism volumes, circle circumference, nets and views. Precision is integrated into practical measurement; circle area is not introduced here.
Official curriculum source ↗