Area of a triangle formula: Area = ½ab sin C
The area of a triangle formula is Area = ½ab sin C.
What each letter means
- \(a,\ b\) two sides of the triangle
- \(C\) the angle between those two sides
When to use it
When you know two sides and the angle between them, so you do not need the height. With a right angle it becomes ½ × base × height, because sin 90° = 1.
Worked example
In triangle \(PQR\), \(PQ=9\) cm, \(PR=12\) cm and angle \(QPR=30^\circ\). Find the area.
- \(\text{Area}=\tfrac12(9)(12)\sin30^\circ=54\times\tfrac12\)
Answer: \(27\text{ cm}^2\)
Common mistake
Using an angle that is not between the two sides you multiply.
On your course
| Course | In the exam |
|---|---|
| Edexcel 4MA1 (Higher) | On the formulae page of the Higher papers |
| Cambridge 0580 | On the list of formulas in Extended papers (Extended only) |
From our own IGCSE Maths formula sheets, in our words. Official: Pearson's 4MA1 specification (PDF, Appendix 5) · Cambridge's 0580 syllabus (PDF).
Practise and revise
Questions
What is the area of a triangle formula?
The area of a triangle formula is Area = ½ab sin C. a, b: two sides of the triangle; C: the angle between those two sides.
Is the area of a triangle (½ab sin C) given in the exam?
Edexcel 4MA1 (Higher): on the formulae page of the Higher papers. Cambridge 0580: on the list of formulas in Extended papers (Extended only). This comes from our own IGCSE Maths formula sheets; your teacher has the official booklet.
Does ½ab sin C work for every triangle?
Yes, as long as C is the angle between sides a and b. It works for acute, obtuse and right-angled triangles.
Our own wording, examples and card, checked by IGCSE Math Revision. Not produced or endorsed by Pearson Edexcel.