For any triangle, area = ½ab sin C, where a and b are two sides and C is the angle between them. This works even when the triangle has no right angle.
With BC = 16 cm, AC = 4 cm and the angle between them 84°, the area is ½ × 16 × 4 × sin 84° = 31.8 cm². The angle must be the one between the two sides you use, called the included angle. Label the triangle carefully before you start.
Worked example
BC = 6 cm, AC = 8 cm and ∠ACB = 97°. Find the area to 1 d.p.
- The angle between the two sides is 97°.
- ½ × 6 × 8 × sin 97° = 23.82…
Answer:23.8 cm²
Key words
- included angle
- the angle between two given sides
- ½ab sin C
- the area formula for any triangle
- non-right-angled
- a triangle with no 90° angle
Practise this
New questions every time.
Common Core-referenced: HSG-SRT.D.9