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Extended Only Trigonometry

Area of a Triangle (1/2 ab sin C) for IGCSE Maths

Finding the area of a triangle using two sides and the included angle. This subtopic is part of Trigonometry in the Cambridge IGCSE Mathematics 0580 syllabus (Extended tier only). Understanding area o

What You Need to Know

Finding the area of a triangle using two sides and the included angle. This subtopic is part of Trigonometry in the Cambridge IGCSE Mathematics 0580 syllabus (Extended tier only). Understanding area of a triangle (1/2 ab sin c) is essential for achieving a strong grade in your IGCSE Maths exam.

Understanding Area of a Triangle (1/2 ab sin C)

The area of any triangle can be calculated using Area = ½ab sin C, where a and b are two sides and C is the included angle between them. This formula is Essential for IGCSE Extended when no perpendicular height is given. It replaces the standard ½ × base × height formula. In Paper 4, it commonly appears as part of a multi-step trigonometry question — finding the area after using the Sine or Cosine Rule to determine a missing side.

Step-by-Step Method

  1. 1

    Identify two sides and the included angle

    You need the two sides that form the angle — the angle must be between the two given sides.

  2. 2

    Write the formula

    Area = ½ × a × b × sin C. Write this before substituting.

  3. 3

    Substitute

    Replace a, b, and C with the given values. The angle must be in degrees (calculator in degree mode).

  4. 4

    Calculate

    Multiply ½ × a × b first, then multiply by sin C. Or use the full expression in one calculator step.

  5. 5

    State units and round

    Area is always in square units (cm², m²). Round to 3 significant figures unless specified otherwise.

Worked Example

Question

Find the area of triangle ABC where AB = 8 cm, BC = 11 cm and angle ABC = 35°.

Solution

Step 1: AB and BC are the two sides, and angle ABC (= 35°) is the included angle between them. Step 2: Area = ½ × AB × BC × sin(ABC) Area = ½ × 8 × 11 × sin 35° Step 3: Calculate. Area = 0.5 × 8 × 11 × 0.5736 Area = 44 × 0.5736 Area = 25.237... cm² Answer: Area = 25.2 cm² (3 s.f.)

Exam Tips for Area of a Triangle (1/2 ab sin C)

  • The angle in the formula must be the angle BETWEEN the two named sides — do not use any other angle.
  • If the angle is obtuse (between 90° and 180°), sin is still positive — the area formula works for all triangles.
  • This formula is on the IGCSE formula sheet — you do not need to memorise it, but you must know when to use it.
  • A common exam question gives you the area and asks you to find a missing angle or side — rearrange the formula before substituting.

Practice Questions

Q1: Triangle PQR has PQ = 6 cm, QR = 9 cm and angle PQR = 48°. Find the area of triangle PQR.

Show hint

Use Area = ½ × 6 × 9 × sin 48°. The angle 48° is between sides PQ and QR.

Q2: A parallelogram has sides 14 cm and 10 cm with an included angle of 70°. Find its area.

Show hint

A parallelogram is made of two identical triangles. Area of parallelogram = 2 × ½ × 14 × 10 × sin 70° = 14 × 10 × sin 70°.

Q3: Triangle ABC has AB = 13 cm, AC = 9 cm and angle BAC = 112°. Find the area.

Show hint

sin 112° is positive (second quadrant). Area = ½ × 13 × 9 × sin 112°.

Frequently Asked Questions

What is area of a triangle (1/2 ab sin c) in IGCSE Maths?

Finding the area of a triangle using two sides and the included angle.

Is area of a triangle (1/2 ab sin c) in the Core or Extended syllabus?

Area of a Triangle (1/2 ab sin C) is part of the Extended only syllabus for IGCSE Mathematics 0580.

How do I revise area of a triangle (1/2 ab sin c) effectively?

Start with the revision notes to understand key concepts, then work through the worked examples step by step. Finally, practise past paper questions under timed conditions. Teacher Rig recommends spending focused revision sessions on area of a triangle (1/2 ab sin c) rather than trying to cover everything at once.

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