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
Two sides of a triangle are 6.3 cm and 4.8 cm, and the angle between them is \(72^\circ\). Find the area.
- \(\text{Area}=\tfrac12(6.3)(4.8)\sin72^\circ\)
Answer: \(14.4\text{ cm}^2\) (3 s.f.)
Common mistake
Using an angle that is not between the two sides you multiply.
On your course
| Course | In the exam |
|---|---|
| AA SL | In the IB formula booklet |
| AI SL | In the IB formula booklet |
| AA HL | In the IB formula booklet |
| AI HL | In the IB formula booklet |
From our own IB Maths formula sheets, in our words. The IB gives its booklet to schools, so we checked against our own copy: your teacher has the official one. Official: IB DP Mathematics page.
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?
AA SL: in the IB formula booklet. AI SL: in the IB formula booklet. AA HL: in the IB formula booklet. AI HL: in the IB formula booklet. This comes from our own IB 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 IB Math Revision. Not produced or endorsed by the International Baccalaureate Organization.