Geometry & MeasuresTopic Summary

Knowledge Organiser: Area of Triangle Using Trigonometry

Part of Area of Triangle (Trig) · GCSE GCSE Mathematics revision

This topic summary covers Knowledge Organiser: Area of Triangle Using Trigonometry within Area of Triangle (Trig) for GCSE Mathematics. Revise Area of Triangle (Trig) in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 2 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 4 of 4 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 4 of 4

Practice

12 questions

Recall

2 flashcards

Knowledge Organiser: Area of Triangle Using Trigonometry

Key Terms
  • Included angle: The angle C that sits BETWEEN sides a and b
  • SAS: Two sides and the included angle — what this formula requires
  • Perpendicular height: The trig formula avoids needing this explicitly
Must-Know Facts
  • Use when you know two sides and the included (between them) angle
  • The angle MUST be between the two known sides
  • If C = 90°, sin 90° = 1 and formula becomes ½ab — the standard right-angle formula
  • Can use any labelling: ½ab sin C = ½bc sin A = ½ac sin B
  • Answer in square units: cm², m²
Key Formula
  • Area = ½ × a × b × sin C
  • where C is the angle BETWEEN sides a and b
  • Use when: two sides + included angle (no height given)
Common Mistakes
  • Angle not between the two sides: C must be the included angle between sides a and b — not any angle in the triangle
  • Forgetting the ½: Area = ½ × a × b × sin C — the ½ is always required
  • Using degrees not radians: Calculator must be in degree mode at GCSE
  • Confusing with ½ base × height: This formula is used when the perpendicular height is not given — both methods give the same answer

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Practice Questions for Area of Triangle (Trig)

What is the trigonometric formula for the area of a triangle with sides a and b and included angle C?

  • A. Area = ab sinC
  • B. Area = ½ab sinC
  • C. Area = ½ab cosC
  • D. Area = ½(a + b) sinC
1 markfoundation

Starting from Area = ½ × base × height, show how to derive the formula Area = ½ab sinC.

2 marksstandard

Quick Recall Flashcards

Trig Area Formula
Area = (1/2)ab sinC. The angle MUST be between the two sides you're using.
Area with Trig
Area = ½ab sin C

12 questions on Area of Triangle (Trig) — practise free

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