Understand the idea.
Perimeter is the distance around
Perimeter is the total length of the boundary around a shape. Trace one complete circuit and count each outside edge once. Internal dividing lines do not belong to that outside boundary. Convert all edge lengths to the same unit before adding.
For a rectangle, opposite sides are equal, so adding the length and width gives half the perimeter. Doubling this sum includes all four sides. Perimeter is a length, so use units such as centimetres or metres rather than square units.
Missing edges and real boundaries
For an irregular rectilinear outline, label missing lengths before adding. A whole horizontal span may equal the sum of several smaller horizontal sections; subtract known sections to find the missing one. Use matching vertical spans in the same way.
In practical boundary problems, decide which parts actually need material. A gate may replace part of a fence, so subtract its width from the complete perimeter. Area answers a different question: how much surface is covered inside the boundary.
See the method in action.
A complete rectangular boundary
Find the perimeter of a rectangle 9 cm long and 4 cm wide.
Worked solution
- 1
List the four outside lengths.
Opposite sides of a rectangle are equal.
- 2
Add the boundary lengths.
The length-width pair occurs twice around the rectangle.
- 3
State the perimeter.
Perimeter measures a distance around the edge.
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?
Worked solution
- 1
Calculate the whole garden boundary.
The complete rectangle contains two lengths and two widths.
- 2
Remove the section occupied by the gate.
The gate occupies two metres of boundary that need no fencing.
- 3
State the required fencing length.
The remaining boundary is the part to be fenced.
36 m of fencing.
Try it yourself.
Check your understanding
A square has side 6.5 cm. What is its perimeter?
Show answer & reasoning
26 cm
A square has four equal boundary lengths. Its perimeter is .
Keep practising
6 worksheet questions · 14 marks
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
cm.
22 cm - A triangle has sides 5 cm, 7 cm and 9 cm. Find its perimeter.1 mark
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 m.
Each width is 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
m; m.
.
m.
32 m - A 10 m by 6 m garden has a 1.5 m gate. Find the fencing length.2 marks
m.
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: cm.
Second perimeter: 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 ↗