Free IB Maths AA SL and AI SL lesson: Area = ½ ab sin C
A ready-to-teach IB Maths AA SL and AI SL lesson on Area = ½ ab sin C: editable slides and teacher notes, free; a printable worksheet in 3 levels with answers for school plans. About 55 minutes.
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One lesson for AA SL and AI SL
Area = ½ ab sin C is taught in IB Maths AA SL and IB Maths AI SL, with the same key ideas. Choose your course above the download button: each version's slides use that course's own worked example, questions and practice link.
- AA SL (Unit 3 · Geometry & Trigonometry)
- AI SL (Unit 3 · Geometry & Trigonometry)
What's inside
- Slides (PowerPoint, editable) · freeabout 12 slides: do now, objectives, key ideas, a worked example step by step, “your turn”, practice QR code, exit ticket
- Teacher notes (PDF) · freelesson plan with timings, common mistakes, homework links
- Worksheet (PDF) · school plans6 questions, 19 marks: Fluency, Reasoning, Exam-style. Included with school plans and the teacher trial.
- Answers (PDF) · school plansthe answer to every worksheet question, from its mark scheme. Included with school plans and the teacher trial.
Learning objectives
- Area of a triangle ½ab sin C
Key ideas on the slides
- Area = ½absin C, where C is the angle between sides a and b.
- With three sides, find an angle with the cosine rule first.
- Rearrange to find an unknown angle: sin C = (2 × Area)/ab, which can give an acute and an obtuse answer.
- The area of a segment is the sector area minus the triangle area ½r²sin θ.
By the end of the lesson, students should be able to answer a question like: Find the area of a triangle with a=6, b=8, and C=30°.
Key vocabulary
- included angle: The angle between the two sides used.
- sector: A slice of a circle between two radii.
- segment: The region between a chord and an arc.
Common mistakes this lesson tackles
- Using an angle that is not between the two sides.
- Forgetting the ½.
- Missing the obtuse answer when finding an angle from an area.
Calculator tips
- Degree mode; round only the final area.
Lesson plan
| 0–5 min | Do now: students write down what they remember about Cosine rule and Sine rule |
| 5–8 min | Share the learning objective and success criteria |
| 8–20 min | Teach: the worked example, step by step; students copy the method |
| 20–25 min | Your turn: 1 mini-whiteboard question; check every board before moving on |
| 25–42 min | Practise: the worksheet (6 questions in 3 levels, with school plans and the teacher trial) or the topic's practice questions online; move up a level after two right in a row |
| 42–47 min | Plenary: 1-question exit ticket; collect it to plan the next lesson |
For students: practise this topic
The worksheet's QR code opens your course's practice questions:
- IB Maths AA SL Unit 3: Non right angled trigonometry practice questions
- IB Maths AI SL Unit 3: Non-Right-Angled Trigonometry practice questions
What schools get
- Set this lesson as homework, marked by AI against the mark scheme, with every result in your markbook (with a School plan).
- This lesson's worksheet in three levels, with its answers, ready to print.
- Support, Core and Stretch versions and A/B copies of the worksheet from the full question bank, in the worksheet builder.
- Create lesson: this lesson rebuilt for your class's next scheme-of-work lesson, from the full bank.
School licences from €490 a year. Try everything free for 30 days as a teacher: no card.
Questions teachers ask
Is this lesson free?
The slides and the teacher notes are free to download with a free IB Math Revision teacher account (sign in with Google, Microsoft or email); no card. The printable worksheet in three levels and its answers are included with school plans and the free 30-day teacher trial.
Can I edit the slides?
Yes. The slides are an ordinary PowerPoint file: change, add or delete anything. They also open in Google Slides and Keynote. The logo and web address sit on the slide master, so your edits do not move them.
What do students use for homework?
The practice slide's QR code and web address take students to the IB Maths AA SL Unit 3: Non right angled trigonometry practice questions on ibmathrevision.com, where the free questions are open and the full bank comes with a plan.