Lesson G23

G23 Area of any triangle using one-half ab sin C Quiz: AQA Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson G23, Area of any triangle using one-half ab sin C: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 4: Geometry and measures, written with Revision Ninja.

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The 20 questions

  1. (H) Which formula gives the area of triangle ABC using sides b and c and the angle A between them?

    • 1/2 bc tan A
    • 1/2 bc sin A
    • bc cos A
    • 2bc sin A

  2. (H) A triangle has sides 8 cm and 10 cm with an included angle of 30 degrees. What is its area in cm^2?

    • 80
    • 40
    • 20
    • 10

  3. (H) A triangle has sides 6 cm and 9 cm with an included angle of 60 degrees. What is its area, to 1 decimal place?

    • 23.4
    • 27.0
    • 54.0
    • 13.5

  4. (H) A triangle has sides 7 cm and 4 cm with an included angle of 150 degrees. What is its area?

    • 7 cm^2
    • 12.1 cm^2
    • 14 cm^2
    • 28 cm^2

  5. (H) What is the area of a triangle with two sides of 5 cm and 12 cm enclosing an angle of 90 degrees?

    • 30 cm^2
    • 17 cm^2
    • 60 cm^2
    • 15 cm^2

  6. (H) A triangle has sides 9 cm and 6 cm and area 27 cm^2. What is the angle between these two sides?

    • 90 degrees
    • 30 degrees
    • 60 degrees
    • 45 degrees

  7. (H) Triangle ABC has a = 10 cm, b = 4 cm and angle C = 25 degrees. What is its area, to 1 decimal place?

    • 20.0 cm^2
    • 8.5 cm^2
    • 17.0 cm^2
    • 4.2 cm^2

  8. (H) A triangle has sides 12 cm and 5 cm with an included angle of 45 degrees. What is its area, to 1 decimal place?

    • 30.0 cm^2
    • 42.4 cm^2
    • 15.0 cm^2
    • 21.2 cm^2

  9. (H) A triangle has sides 8 cm and 5 cm with an included angle of 120 degrees. What is its area, to 1 decimal place?

    • 20.0 cm^2
    • 8.7 cm^2
    • 34.6 cm^2
    • 17.3 cm^2

  10. (H) A triangle has area 20 cm^2, and two of its sides are 8 cm and 10 cm. What is the sine of the angle between these two sides?

    • 0.25
    • 0.5
    • 0.8
    • 2.5

  11. (H) Triangle PQR has PQ = 6 cm, QR = 10 cm and angle Q = 40 degrees. What is its area, to 1 decimal place?

    • 38.6 cm^2
    • 30.0 cm^2
    • 60.0 cm^2
    • 19.3 cm^2

  12. (H) Two sides of a triangle are 15 cm and 4 cm, and the included angle is 20 degrees. What is its area, to 1 decimal place?

    • 20.5 cm^2
    • 5.1 cm^2
    • 60.0 cm^2
    • 10.3 cm^2

  13. (H) A triangle has sides 10 cm and 20 cm and area 40 cm^2. What is the sine of the angle between the two sides?

    • 0.8
    • 0.2
    • 4.0
    • 0.4

  14. (H) A triangle has sides 5 cm and 8 cm with an included angle of 150 degrees. What is its area?

    • 20 cm^2
    • 10 cm^2
    • 5 cm^2
    • 34.6 cm^2

  15. (H) Triangle XYZ has XY = 14 cm, YZ = 9 cm and angle Y = 65 degrees. What is its area, to 1 decimal place?

    • 63.0 cm^2
    • 28.5 cm^2
    • 57.1 cm^2
    • 126.0 cm^2

  16. (H) Two sides of a triangle are 6 cm each, with an included angle of 60 degrees. What is its area, to 1 decimal place?

    • 15.6 cm^2
    • 18.0 cm^2
    • 7.8 cm^2
    • 36.0 cm^2

  17. (H) A triangle has area 30 cm^2 with a = 10 cm and angle C = 60 degrees. What is side b to 1 decimal place?

    • 8.7 cm
    • 6.9 cm
    • 3.5 cm
    • 12.0 cm

  18. (H) A triangle has area 36 cm^2 with sides 12 cm and 8 cm. What is the acute included angle to 1 decimal place?

    • 22.5 degrees
    • 60.0 degrees
    • 48.6 degrees
    • 41.4 degrees

  19. (H) A triangle has sides 6 cm and 10 cm with area 15 cm^2. What is the smallest possible included angle?

    • 30 degrees
    • 90 degrees
    • 15 degrees
    • 60 degrees

  20. (H) Triangle ABC has AB = 10 cm, AC = 12 cm and angle A = 150 degrees. What is its area?

    • 15 cm^2
    • 103.9 cm^2
    • 60 cm^2
    • 30 cm^2

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