Area of Triangle (Trig), Knowledge Organiser

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
• Wrong calculator mode: The 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

Worked Examples

Find the area of a triangle with sides 6cm and 8cm and an included angle of 45°. Solution Area = (1/2) × 6 × 8 × sin 45° Area = 24 × (√2/2) = 12√2 Area = 16.97 cm² (2 d.p.)