DfE statement G23 · Geometry and measures

Area of a triangle: ½ab sin C

Higher onlyCalculator

Area of a triangle: ½ab sin C is content statement G23 of the DfE GCSE mathematics subject content, in the geometry area. It is Higher tier only, and it is normally a calculator-paper question. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.

What the specification says

The DfE subject content for GCSE mathematics states, verbatim: "Know and apply Area = ½ ab sin C to calculate the area, sides or angles of any triangle." (statement G23). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement G23

Tier

Higher tier only. A Foundation entry is never asked for this, so if you are sitting Foundation you can leave it out of your revision entirely.

Calculator

This is calculator work, which places it on Papers 2 and 3. Know your own calculator before the exam, keep full accuracy through the working and round only at the end.

Common mistakes

Using an angle that is not between the two sides. In ½ab sin C, C must be the angle enclosed by a and b.
Forgetting the ½, which doubles the area.
Working in radians instead of degrees.

Formulae for this statement

Area of a triangle using sineArea = ½ ab sin CYou must know this

Sample questions (10 of 30)

G23 · Area of a triangle: ½ab sin CQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Geometry and measures

G23

Advanced

Which of these statements about the area formula Area = 1/2ab sin C is correct?

💡 Hints:

Higher worksheet Higher geometry and measures practice

Nearby statements

G1Geometric terms, notation and diagrams G2Ruler and compass constructions and loci G3Angle facts, parallel lines and polygons G4Properties of triangles and quadrilaterals

Questions people ask

Is area of a triangle: ½ab sin C on Foundation or Higher?

Higher only. Foundation papers do not ask for it.

Can I use a calculator for area of a triangle: ½ab sin C?

Yes, on Papers 2 and 3, which are the calculator papers and where questions on this usually sit. Paper 1 is non-calculator.

What is the single most common mistake here?

Using an angle that is not between the two sides. In ½ab sin C, C must be the angle enclosed by a and b.

Are these past paper questions?

No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.

Back to Geometry and measures at Foundation or at Higher.