Example 1
Find a triangle area
- Identify base 12 cm and perpendicular height 7 cm.
- Use A=½bh.
- Calculate ½×12×7.
- Attach square units.
Final answer: 42 cm²
Check: Two copies form a 12×7 parallelogram of area 84 cm².
What students learn in AC9M7M01
We are learning to solve problems involving the area of triangles and parallelograms using established formulas and appropriate units.
Triangle and parallelogram area depends on a chosen base and its perpendicular height, not on an arbitrary sloping side. Area is measured in square units.
A parallelogram has area bh; rearranging or duplicating a triangle shows that its area is half the matching parallelogram, A=½bh.
For composite regions, partition or subtract non-overlapping pieces with compatible dimensions. Verify by using a second decomposition that covers the same region exactly once.
Success criteria
- I can identify a valid base and perpendicular height.
- I can calculate triangle and parallelogram areas with square units.
- I can solve and independently check a composite-area problem.
Key vocabulary
- perpendicular height
- shortest distance at right angles to the base.
- base
- chosen side used with a corresponding height.
- square unit
- unit measuring area.
Visual models and representations
Use these models to connect the mathematical idea to values, diagrams, coordinates, graphs or structure before moving to symbolic calculation.
4 worked numerical & application examples
Follow each example from representation and setup through calculation/reasoning, interpretation and an independent check.
Example 2
Find a composite area
- Start with a 10×8 rectangle.
- Find its area as 80 cm².
- Subtract the 3×4 cut-out of 12 cm².
- State the remaining area.
Final answer: 68 cm²
Check: Add non-overlapping rectangles 7×8 and 3×4 to get 68 cm².
Example 3
Application problem 1
Problem: A parallelogram has base 12 cm and perpendicular height 7 cm. A triangle with base 8 cm and height 5 cm is cut from it. Find the remaining area and state the correct units.
- Plan: Represent the information first, then calculate, interpret and independently check the result.
- Work: Parallelogram area = 84 cm²; triangle area = 20 cm²; remaining area = 64 cm².
- Interpret: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Final answer: Parallelogram area = 84 cm²; triangle area = 20 cm²; remaining area = 64 cm².
Check: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Example 4
Application problem 2
Problem: A parallelogram and triangle share base 14 cm and height 5 cm. Compare areas.
- Plan: Apply both formulas to the same base-height pair.
- Work: The parallelogram area is 14×5=70 cm² and the triangle area is ½×14×5=35 cm², so their areas compare in the ratio 2:1.
- Interpret: The complete model for “A parallelogram and triangle share base 14 cm and height 5 cm. Compare areas.” shows The parallelogram area is 14×5=70 cm² and the triangle area is ½×14×5=35 cm², so their areas compare in the ratio 2:1.
Final answer: The parallelogram area is 14×5=70 cm² and the triangle area is ½×14×5=35 cm², so their areas compare in the ratio 2:1.
Check: The complete model for “A parallelogram and triangle share base 14 cm and height 5 cm. Compare areas.” shows The parallelogram area is 14×5=70 cm² and the triangle area is ½×14×5=35 cm², so their areas compare in the ratio 2:1.
Common misconceptions
Common mistake: Sloping side used as height.
Correction: Locate or construct the perpendicular distance.
Common mistake: Triangle factor one-half omitted.
Correction: Two congruent triangles form a parallelogram.
Common mistake: Mixed length units multiplied.
Correction: Convert first.
10 important problems to solve
Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.
1. Find the area of a parallelogram with base 9 cm and height 4 cm.
Check answer
Answer: 36 cm².
Hint: Multiply base by perpendicular height.
Why: Using the method “Multiply base by perpendicular height.” gives 36 cm².
2. Find the area of a triangle with base 10 m and height 6 m.
Check answer
Answer: 30 m².
Hint: Use one-half times base times height.
Why: Using the method “Use one-half times base times height.” gives 30 m².
3. Which unit measures area when lengths are metres?
Check answer
Answer: Square metres, m².
Hint: Identify area as a two-dimensional measure, then choose square units.
Why: Using the method “Area is two-dimensional.” gives Square metres, m².
4. A triangle has area 24 cm² and base 8 cm. Find its height.
Check answer
Answer: 6 cm.
Hint: Use h=2A÷b.
Why: Using the method “Use h=2A÷b.” gives 6 cm.
5. Find the area of a parallelogram with base 7.5 m and height 3 m.
Check answer
Answer: 22.5 m².
Hint: Use the perpendicular height.
Why: Using the method “Use the perpendicular height.” gives 22.5 m².
6. A 12×9 rectangle loses a 4×3 corner. Find remaining area.
Check answer
Answer: 96 square units.
Hint: Subtract the cut-out once.
Why: Using the method “Subtract the cut-out once.” gives 96 square units.
7. Why is a 6 cm sloping side not automatically a triangle height?
Check answer
Answer: A triangle height is the perpendicular distance to the chosen base; a 6 cm sloping side is a valid height only if it meets that base at 90°.
Hint: Look for a right-angle relationship.
Why: The reasoning for “Why is a 6 cm sloping side not automatically a triangle height?” is complete because A triangle height is the perpendicular distance to the chosen base; a 6 cm sloping side is a valid height only if it meets that base at 90°.
8. A triangular garden has area 54 m² and height 9 m. Find its base.
Check answer
Answer: From 54=½×b×9, multiply by 2 and divide by 9 to get b=108÷9=12 m; checking gives ½×12×9=54 m².
Hint: Rearrange b=2A÷h.
Why: The complete model for “A triangular garden has area 54 m² and height 9 m. Find its base.” shows From 54=½×b×9, multiply by 2 and divide by 9 to get b=108÷9=12 m; checking gives ½×12×9=54 m².
9. A parallelogram and triangle share base 14 cm and height 5 cm. Compare areas.
Check answer
Answer: The parallelogram area is 14×5=70 cm² and the triangle area is ½×14×5=35 cm², so their areas compare in the ratio 2:1.
Hint: Apply both formulas to the same base-height pair.
Why: The complete model for “A parallelogram and triangle share base 14 cm and height 5 cm. Compare areas.” shows The parallelogram area is 14×5=70 cm² and the triangle area is ½×14×5=35 cm², so their areas compare in the ratio 2:1.
10. A parallelogram has base 12 cm and perpendicular height 7 cm. A triangle with base 8 cm and height 5 cm is cut from it. Find the remaining area and state the correct units.
Check answer
Answer: Parallelogram area = 84 cm²; triangle area = 20 cm²; remaining area = 64 cm².
Hint: Represent the information first, then calculate, interpret and independently check the result.
Why: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Curriculum coverage and elaborations
Content description: solve problems involving the area of triangles and parallelograms using established formulas and appropriate units.
International curriculum mapping
The Australian Curriculum code above is exact. Victorian Year 7, NSW Stage 4, US Grade 7, England Key Stage 3, New Zealand Level 4 and comparable international curricula contain broadly related learning, but code-to-code equivalence varies by jurisdiction.
🎥 Optional Video Lesson
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
- Pause after each worked example.
- Try the examples yourself.
- Return to the SkillrHub lesson before continuing.
Recommended: Area
Math Antics — Review how area is measured and calculated; then use the topic lesson for triangle and parallelogram formulas.
As you watch: How does counting square units lead to an area calculation?
Load video player Loads YouTube in this lesson. See the video notice below.
Try it: Rearrange a drawn parallelogram into a rectangle and explain why the perpendicular height matters.
Video unavailable, inaccurate or unsuitable for this year? Report a video problem to SkillrHub by email. You can continue with the written lesson and practice resources.
About these videos
Videos are curated from trusted independent educational creators and played through YouTube. Rights remain with their respective owners. Inclusion does not imply that a creator or YouTube endorses SkillrHub.
YouTube’s terms and privacy policy apply to its player. Advertising, recommendations and external links may appear, and videos may change or become unavailable. SkillrHub’s written lessons and practice resources remain available separately.
To report a content, suitability or rights concern, email skillrhublearning@gmail.com with the lesson code and video link. Please do not include personal student information.
Curriculum equivalents: Victoria, NSW and international
Curriculum equivalents for Solve problems involving the area of triangles and parallelograms using...
Mapped skill: solve problems involving the area of triangles and parallelograms using established formulas and appropriate units
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M7M01 · Year 7 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M7M01 · Level 7 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA4-ARE-C-01 · Stage 4 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 7 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 7 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 8, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 7 |
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
Help improve SkillrHub
Questions or feedback?
Ask about this lesson, suggest an improvement or report an error. Facebook opens only when you choose an option below.
Topic reference: AC9M7M01 — Area of Triangles and Parallelograms
Privacy: Please don’t share personal student or school information. Younger students should ask a parent, guardian or teacher to post on their behalf.