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
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.
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