You will learn
- Identify base and height.
- Use area = ½ × b × h.
- Find a missing height.
- Solve triangle problems.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Area of a triangle = ½ × base × height.
- Height is perpendicular to the base.
- Area is in square units.
- Rearrange to find a missing height.
Words to know
Side the height is measured to.
Perpendicular distance.
Surface covered.
Unit of area.
1. Discover: half a rectangle
A triangle has base 10 cm and height 6 cm. Why is its area half of 10 × 6?
2. Understand: area of triangles
- A triangle is half of a rectangle or parallelogram with the same base and height.
- Area = ½ × base × height = ½ × 10 × 6 = 30 cm².
- Base 8, height 5: 20. Base 12, height 7: 42.
- Area 24 and base 8: ½ × 8 × h = 24, so h = 6.
Idea 1: Formula
Base 10, height 6: ½ × 10 × 6 = 30 cm². Base 8, height 5: 20 cm².
Idea 2: More
Base 12, height 7: 42 cm². Base 9, height 4: 18 cm².
Idea 3: Missing height
A = 24, b = 8: 24 = ½ × 8 × h = 4h, so h = 6 cm.
Why half? Two triangles make a rectangle b × h.
3. Worked examples
Example 1 (I show you): Area
b = 10, h = 6
- ½ × 10 × 6.
Answer: 30 cm²
Example 2 (We do it together): Area
b = 9, h = 4
- ½ × 9 × 4.
Answer: 18 cm²
Example 3 (You try): Height
A = 24, b = 8
Show the steps and answer
- 4h = 24.
Answer: 6 cm
Did you know?
The height must be at right angles to the base, not along a slanting side.
Why this matters
Triangle area is used in roofs, sails and land plans.
4. Explore: area
You need paper.
- Find base and height.
- Multiply them.
- Halve.
- Write cm².
Think about it: what did you notice?
30 cm².
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- Area = ½ × ___ × ___.
- The base is ___ and the height is ___.
- The area is ___ cm².
- The missing height is ___.
Guided practice
Question 1. ½ × 10 × 6?
30.
Question 2. ½ × 12 × 7?
42.
Question 3. Height if area 24, base 8?
6.
Independent practice
Level 1: Start
- b 10, h 6
- b 8, h 5
- b 12, h 7
- b 9, h 4
- Height if A = 24, b = 8
Level 2: Grow
- b 6, h 4
- b 14, h 5
- b 7, h 6
Level 3: Stretch
- Right-angled triangle with legs 6 and 8
- Height if A = 35, b = 10
- Ben says b 9, h 4 gives 36 cm². What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A triangle has base 10 cm and height 6 cm. Area?
Show a sample answer
30 cm².
Another one. A triangular flag has base 40 cm and height 30 cm. Find its area.
Show a sample answer
600 cm²
7. Common mistakes
Fix: Halve b × h.
Fix: A triangle is half of b × h.
Fix: Use the perpendicular height.
8. Lesson summary and revision card
- I can identify base and height.
- I can use area = ½ × b × h.
- I can find a missing height.
- I can solve triangle problems.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- ½ × b × h.
- Height is perpendicular.
- Answer in square units.
11. Next lesson
Next lesson: Area of parallelograms. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Find the area of a triangle with base 10 cm and height 6 cm. [3 marks]
- Find the area with base 8 cm and height 5 cm. [2 marks]
- Find the area with base 12 cm and height 7 cm. [2 marks]
- A triangle has area 24 cm² and base 8 cm. Find the height. [3 marks]
- Ali says base 9 cm and height 4 cm gives 36 cm². Is he right? Explain. [3 marks]
Total: 13 marks.
Marking guide and model answers
- Area = ½ × b × h [1]; ½ × 10 × 6 [1]; 30 cm² [1]
- ½ × 8 × 5 [1]; 20 cm² [1]
- ½ × 12 × 7 [1]; 42 cm² [1]
- 24 = ½ × 8 × h = 4h [1]; h = 24 ÷ 4 [1]; 6 cm [1]
- No [1]. 9 × 4 = 36 is a rectangle; a triangle is half [1]. 18 cm² [1].
Score guide: 12 to 13 = secure. 8 to 11 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- b 10, h 6
- b 8, h 5
- b 12, h 7
- b 9, h 4
- Height if A = 24, b = 8
- b 10, h 6
- b 8, h 5
- b 12, h 7
- b 9, h 4
- Height if A = 24, b = 8
Homework
Cut a rectangle diagonally and show two triangles.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| b 10, h 6 | 30 | 2 |
| b 8, h 5 | 20 | 2 |
| b 12, h 7 | 42 | 2 |
| b 9, h 4 | 18 | 2 |
| Height if A = 24, b = 8 | 6 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 30; 2 20; 3 42; 4 18; 5 6.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 30 cm²; 7 20 cm²; 8 42 cm²; 9 18 cm²; 10 6 cm.
Independent practice answers. Level 1: 1 30 cm²; 2 20 cm²; 3 42 cm²; 4 18 cm²; 5 6 cm. Level 2: 1 12 cm²; 2 35 cm²; 3 21 cm². Level 3: 1 24 cm²; 2 7 cm; 3 He forgot the half: ½ × 9 × 4 = 18 cm²..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Identify base and height | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Use area = ½ × b × h | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Find a missing height | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Solve triangle problems | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Forgetting to halve. Halve b × h.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Area of rectangles.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child finds the area of triangles. You do not need to be good at mathematics to help.
- Cut a rectangle diagonally.
- Ask: what is the perpendicular height?
- Remember to halve.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: identify base and height; use area = ½ × b × h; find a missing height; solve triangle problems.
Prerequisite knowledge. Area of rectangles.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 45–60 minutes. It can be split into two shorter sessions.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need paper. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Key questions. What is the base? What is the perpendicular height?
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Forgetting to halve. Halve b × h.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 13-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Area of rectangles. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
This lesson is based on the sources below, and no official endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 6 » Ratios & Proportional Relationships; Grade 6 » Geometry. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 6.G.A.1; Cambridge Primary Mathematics Stage 6 (area of triangles). These sources informed the lesson.