Australian Curriculum v9 / ACiQ Year 7 Mathematics - Unit 0 - Perimeter and area of common shapes
Perimeter and area of common shapes
Solve perimeter and area problems for rectangles, parallelograms and triangles using appropriate units.
Updated 2026-07-24 - 6 min read
Solve perimeter and area problems for rectangles, parallelograms and triangles using appropriate units. This draft teaching resource is aligned to the cited Year 7 content descriptions and still requires named human curriculum approval.
Name what each length, angle, coordinate or view represents before choosing a formula or transformation; the diagram and units are part of the reasoning.
1. Measure boundaries and regions
Perimeter measures distance around a boundary; area measures the region inside. Triangle area is half the related parallelogram area.
Text-equivalent representation: Triangle text schematic: a 10 cm horizontal base; a 7 cm perpendicular segment from the opposite vertex to the base, marked with a right-angle symbol. The sloping side is not the height.
Decision check: Apply this lesson's rule to the worked example: Convert all lengths to the same unit and use perpendicular height for area. Identify the exact value, label or property that satisfies the rule.
Worked examples with complete reasoning
Worked example 1
Question: Find the perimeter of a rectangle 7 m by 3 m.
- Perimeter is the distance around: 2(7 + 3).
- The perimeter is 20 m.
Answer: 20
Check: Perimeter uses length units, not square units.
Worked example 2
Question: Find the area of a rectangle with length 8 cm and width 5 cm. Give the answer in cm².
- Choose the rectangle area formula.
- 8 × 5 = 40 cm².
Answer: 40
Check: Area uses square units and perpendicular height where relevant.
Worked example 3
Question: A parallelogram has area 48 cm² and base 8 cm. Find its perpendicular height.
- Use 48 = 8 × h.
- Divide area by base: h = 6 cm.
Answer: 6
Check: Rearrange the same area formula using inverse operations.
Method map for this topic
- Measure boundaries and regions: Convert all lengths to the same unit and use perpendicular height for area.
Common mistakes and how to correct them
- area formula: Not yet. Area uses square units and perpendicular height where relevant. Recheck the area formula step, then try again.
- area vs perimeter: Not yet. Perimeter uses length units, not square units. Recheck the area vs perimeter step, then try again.
- triangle half: Not yet. The triangle occupies half the matching parallelogram. Recheck the triangle half step, then try again.
- missing dimension: Not yet. Rearrange the same area formula using inverse operations. Recheck the missing dimension step, then try again.
- area rearrangement: Not yet. Use a cut-and-rearrange or equal-halves relationship to connect the shape to a known area formula. Recheck the area rearrangement step, then try again.
- mixed units: Not yet. Convert measurements to the same unit before multiplying. Recheck the mixed units step, then try again.
Practice
- Find the perimeter of a rectangle 7 m by 3 m.
- Find the perimeter of a rectangle 12 m by 5 m.
- Find the area of a rectangle with length 8 cm and width 5 cm. Give the answer in cm².
- Find the area of a parallelogram with base 12 cm and perpendicular height 4 cm. Give the answer in cm².
- A parallelogram has area 48 cm² and base 8 cm. Find its perpendicular height.
- A triangle has area 35 cm² and base 10 cm. Find its perpendicular height.
<details> <summary>Answers and reasoning</summary>
- 20 — Perimeter is the distance around: 2(7 + 3). The perimeter is 20 m.
- 34 — Perimeter is the distance around: 2(12 + 5). The perimeter is 34 m.
- 40 — Choose the rectangle area formula. 8 × 5 = 40 cm².
- 48 — Choose the parallelogram area formula. 12 × 4 = 48 cm².
- 6 — Use 48 = 8 × h. Divide area by base: h = 6 cm.
- 7 — Use 35 = 1/2 × 10 × h. Double the area, then divide by the base: h = 7 cm.
</details>
Checklist and vocabulary
| Skill | Observable evidence | | --- | --- | | distinguish perimeter area units | Distinguish perimeter from area and select appropriate linear or square units. | | apply triangle parallelogram area formulas | Apply established triangle and parallelogram area formulas using perpendicular height. | | explain area relationships and solve | Explain triangle and parallelogram area relationships using rearrangement, then solve missing-dimension or unit-conversion problems. |
Retrieval prompts
- State the defining relationship for each method above without looking.
- Give one example where two visually similar representations mean different things.
- Diagnose one misconception from the list and explain the first corrective step.
- Name a check that is independent of simply repeating the same calculation.
Teach-back and self-check
Close the worked examples and explain perimeter and area of common shapes as if you were helping another Year 7 student. Begin by naming the clue that tells you which relationship, representation or operation is needed. Then show one complete example with labels and units where they matter. At each line, explain what stayed equivalent and why the next step is allowed.
Use this four-part check before calling the method secure:
- Identify: What information is given, and what must be found or justified?
- Represent: Which number line, diagram, table, expression, graph or organised list makes the relationship visible?
- Reason: Which rule connects the representation to the required answer?
- Verify: Can you check by estimation, substitution, an inverse operation, a second representation or the original context?
If the explanation depends on “I just knew”, return to the method map and name the missing decision. A durable method is one you can explain, check and use in a changed context after a delay.
Transfer task
Sketch or describe a real object or layout that uses perimeter and area of common shapes. Label every necessary dimension, coordinate, axis or view, solve the stated problem, and name one limitation of the representation.