AQA GCSE Maths

Area of a triangle (½ab sin C)

AQA GCSE Maths revision on Area of a triangle (½ab sin C). Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.

Sample questions (3 of 16)

  1. Question 1

    In the formula 0.5ab sin C, what is the geometric requirement for the angle C?

    • A) It must be a right angle
    • B) It must be the angle between sides a and b
    • C) It must be the smallest angle in the triangle
    • D) It must be the angle opposite the longest side
    Show answer

    Answer: It must be the angle between sides a and b

    The formula relies on the sine of the angle trapped between the two sides being multiplied. If the angle is not the included one, the formula fails to represent the height of the triangle relative to the chosen base.

  2. Question 2

    A student attempts to calculate the area of a triangle given two sides and an angle that is NOT between them. Which concept should they use first to find the missing angle or side?

    • A) Pythagoras' theorem
    • B) Sine rule
    • C) Circle theorems
    • D) Area of a rectangle
    Show answer

    Answer: Sine rule

    The area formula 0.5ab sin C requires the SAS configuration. If the angle provided is not the included angle, you must use the Sine rule to solve for a missing angle or side before the area can be calculated.

  3. Question 3

    If you are given all three sides of a triangle (SSS) but no angles, why can you not use the 0.5ab sin C formula immediately?

    • A) Because you need at least one angle
    • B) Because the area is zero
    • C) Because sine cannot be used with sides
    • D) Because you must use the area of a circle formula
    Show answer

    Answer: Because you need at least one angle

    The formula explicitly requires an angle C. With only side lengths, you would first need to use the Cosine rule to determine the size of one of the interior angles before you can proceed with the area calculation.

Want to test yourself on the remaining cards for this topic?

13 more questions on Area of a triangle (½ab sin C) — plus mistakes tracking and spaced repetition across the whole Maths spec.

Start a free session → Already have an account? Log in

More AQA Maths topics