Area rule

Area = ½ab sin C, using two sides and the angle between them. CAPS Grade 11 definition, worked example and related trigonometry practice.

Area = ½ab sin C, using two sides and the angle between them.

Definition

The area rule gives the area of any triangle from two sides and the included angle: Area = ½ab sin C. It replaces ½ × base × height when the perpendicular height isn't known.

Worked example

A triangle with sides 7 cm and 10 cm and an included angle of 120° has area ½ × 7 × 10 × sin 120° ≈ 30.31 cm².

With PQ = 10 cm, PR = 6 cm and P̂ = 30°: Area = ½ × 10 × 6 × ½ = 15 cm².

Where it appears in the exam

Area rule is part of the trigonometry section of CAPS Grade 11 Mathematics and is examined in Paper 2 of the November exam.

Step-by-step method

  1. Identify two sides and the angle between them.
  2. Substitute into Area = ½ab sin C.
  3. Calculate with your calculator in degrees.
  4. Give the answer in square units.

Common mistake

Using an angle that is not between the two given sides.

Related trigonometry terms

Frequently asked questions

What does area rule mean in Grade 11 Maths?

The area rule gives the area of any triangle from two sides and the included angle: Area = ½ab sin C. It replaces ½ × base × height when the perpendicular height isn't known.

Which paper tests area rule in Grade 11?

Area rule belongs to the Trigonometry section of CAPS Grade 11 Mathematics, which is examined in Paper 2 of the November exam.

How do I practise questions involving area rule?

Snap a question that uses area rule into Snap&Learn with your grade set to Grade 11, or work through the Grade 11 topic guide and practice papers.

Snap&Learn gives South African Matric learners instant, CAPS-aligned, step-by-step Mathematics solutions. Snap or upload a question and the AI shows every method mark the way the NSC memo awards them. Your first three AI solutions are free.