Lesson G23

G23 know and apply Area = ab sin C to calculate the area, sides or angles of any triangle Quiz: Pearson Edexcel Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson G23, know and apply Area = ab sin C to calculate the area, sides or angles of any triangle: 20 multiple choice questions for the Pearson Edexcel GCSE Maths (1MA1), Unit 4: Geometry and measures, written with Revision Ninja.

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The 20 questions

  1. Which formula gives the area of a triangle with sides a and b and included angle C?

    • ½ab cos C
    • ½ab sin C
    • ab sin C
    • ½(a + b) sin C

  2. In the formula Area equals half ab sin C, what does C represent?

    • Right angle
    • Perpendicular height
    • Hypotenuse
    • Included angle

  3. Sides of 4 cm and 6 cm have an included angle of 90°. What is the area?

    • 10 cm²
    • 24 cm²
    • 6 cm²
    • 12 cm²

  4. Sides of 8 cm and 5 cm have an included angle of 30°. What is the area?

    • 40 cm²
    • 8.7 cm²
    • 20 cm²
    • 10 cm²

  5. Sides of 7 cm and 9 cm have an included angle of 115°. What is the area to 1 decimal place?

    • 34.2 cm²
    • 28.5 cm²
    • 14.2 cm²
    • 63.0 cm²

  6. A triangle has area 24 cm² and two sides of 8 cm and 12 cm. What is the acute included angle?

    • 15°
    • 60°
    • 30°
    • 45°

  7. Two sides a and b enclose an angle of 60°, with b = 10 cm, and the triangle has area 30 cm². What is a to 1 decimal place?

    • 6.9 cm
    • 15.0 cm
    • 10.4 cm
    • 3.5 cm

  8. An isosceles triangle has two equal sides of 10 cm with apex angle 40°. What is its area to 1 decimal place?

    • 16.1 cm²
    • 19.7 cm²
    • 64.3 cm²
    • 32.1 cm²

  9. Sides of 4 cm and 9 cm have an included angle of 150°. What is the area?

    • 36 cm²
    • 18 cm²
    • 9 cm²
    • 15.6 cm²

  10. Two sides of 120 m and 150 m enclose an angle of 35°. What is the area of the plot?

    • 2580 m²
    • 9000 m²
    • About 5160 m²
    • 10 320 m²

  11. Triangle sides are 7 cm, 10 cm and 12 cm. What is its area to 1 decimal place?

    • 35.0 cm²
    • 17.5 cm²
    • 42.0 cm²
    • 70.0 cm²

  12. A triangle has area 36 cm² and two sides of 9 cm and 12 cm. What is sin C to 2 decimal places?

    • 1.33
    • 0.67
    • 0.33
    • 0.75

  13. When the included angle is 90°, what does ½ab sin C reduce to?

    • ½ab
    • ab
    • a² + b²
    • ½(a + b)

  14. Sides of 8 cm and 6 cm have an included angle of 120°. What is the area to 1 decimal place?

    • 20.8 cm²
    • 10.4 cm²
    • 41.6 cm²
    • 24.0 cm²

  15. A triangle has sides 5 cm and 8 cm and area 15 cm². What is the acute included angle to 1 decimal place?

    • 131.4°
    • 75.5°
    • 41.4°
    • 48.6°

  16. Two sides of 15 cm and 20 cm enclose an angle of 25°. What is the area to 1 decimal place?

    • 31.7 cm²
    • 126.8 cm²
    • 63.4 cm²
    • 35.0 cm²

  17. Two sides of 13 cm and 14 cm enclose an angle of 60°. What is the area to 1 decimal place?

    • 78.8 cm²
    • 91.0 cm²
    • 157.6 cm²
    • 45.5 cm²

  18. A triangle has area 40 cm² and sides 9 cm and 11 cm. What is sin C to 2 decimal places?

    • 0.57
    • 1.23
    • 0.44
    • 0.81

  19. A triangle has area 100 cm² and sides 20 cm and 30 cm. What is the acute included angle to 1 decimal place?

    • 19.5°
    • 160.5°
    • 35.3°
    • 70.5°

  20. A triangle has sides of 6 cm and 8 cm and an area of 24 cm². What is the size of the angle between these two sides?

    • 45°
    • 30°
    • 60°
    • 90°

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