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. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. 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.
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
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?
Starting from Area = ½ × base × height, show how to derive the formula Area = ½ab sinC.
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