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4MA1/2H Jan 2019, Question 15: Area of a Parallelogram and Trapezium

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks

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The question, in short

Trapezium with parallel sides (x + 5) and (3x − 2), height (2x − 3) cm, area 133 cm². Show the given quadratic and find x.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 3 marks

Use the trapezium area formula with the given expressions and 133 cm² to derive 8x² − 6x − 275 = 0.

  1. 1Sum of parallel sides: (x + 5) + (3x − 2) = 4x + 3
  2. 2Area = ½(4x + 3)(2x − 3) = 133
  3. 3Expand: (4x + 3)(2x − 3) = 8x² − 6x − 9
  4. 4So 8x² − 6x − 9 = 266
  5. 5Subtract 266: 8x² − 6x − 275 = 0

Answer½(4x + 3)(2x − 3) = 133, so 8x² − 6x − 9 = 266, giving 8x² − 6x − 275 = 0

Part (b) · 3 marks

Solve the quadratic from part (a) to find x, showing working clearly.

  1. 1Solve 8x² − 6x − 275 = 0 with the quadratic formula
  2. 2x = (6 ± √(36 + 4 × 8 × 275)) / 16 = (6 ± √8836) / 16
  3. 3√8836 = 94, so x = 100/16 or x = −88/16
  4. 4x = 6.25 or x = −5.5
  5. 5A length cannot be negative, so x = 6.25

Answer6.25

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