The idea, step by step
Around and inside
The boundary is the line around a shape. Its interior is the space inside that line. A fence follows a boundary; grass covers an interior. The names tell us what to measure, even before we calculate.
Choose the useful measure
Perimeter measures the whole boundary using length units such as centimetres. Area measures the inside using square units. Ask whether the job travels around an edge or covers a surface. A rectangle has four boundary sides, but its area is not found by adding those sides.
A common trap
Adding the side lengths tells us the space inside.
Instead: Adding boundary lengths gives perimeter. Covering or counting square units gives area.
See the thinking
A frame
A photo needs a frame around its edge. Do we need its perimeter or its area?
- A frame follows the outside edge.
- The complete distance along that edge is the perimeter.
A covered board
A rectangular board is 4 unit squares across and 3 squares down. How much space does it cover?
- Count 4 squares in each row.
- There are 3 rows: 4 + 4 + 4 = 12.
- Each piece is a square unit, so report square units.
Check your understanding
Would you measure perimeter or area to buy a carpet?
Show answer
Area.
A carpet covers the inside surface of the floor.
Your turn
6 questions · 7 marks · Work at your own pace.
Read the questions online
- A garden needs edging all the way around. Which measure is needed?1 mark
- A wall will be painted. Which measure describes the surface to paint?1 mark
- Name the part of a shape that separates its inside from its outside.1 mark
- Which unit fits an area: centimetres or square centimetres?1 mark
- A 3 by 2 grid is completely shaded. Find its area.1 mark
- A student says, “The area of a square is the length of its fence.” Explain the error.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A garden needs edging all the way around. Which measure is needed?1 mark
Edging follows the whole boundary.
Perimeter. - A wall will be painted. Which measure describes the surface to paint?1 mark
Paint covers the wall interior.
Area. - Name the part of a shape that separates its inside from its outside.1 mark
The boundary runs around the edge.
The boundary. - Which unit fits an area: centimetres or square centimetres?1 mark
Area counts square units that cover a surface.
Square centimetres. - A 3 by 2 grid is completely shaded. Find its area.1 mark
There are 3 squares in each of 2 rows.
3 + 3 = 6 square units.
6 square units. - A student says, “The area of a square is the length of its fence.” Explain the error.2 marks
A fence follows the boundary rather than covering the surface.
The fence length is perimeter; area is the space inside.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Boundary/interior; measuring perimeter; covering/counting/estimating area; comparing shapes.
Official curriculum source ↗