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0580/32 Feb/Mar 2022, Question 3: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 13 marks

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The question, in short

Use the 1 cm² grid diagram with quadrilaterals A, B, C to name B, find its area with units, measure angle w, and describe transformations mapping A to B and A to C.

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

Part (aia) · 1 mark

State the mathematical name of quadrilateral B.

  1. 1B has one pair of parallel sides (y = 10 and y = 6)
  2. 2Trapezium

AnswerTrapezium

Part (aib) · 3 marks

Calculate the area of quadrilateral B and give the correct units.

  1. 1Parallel sides: 10 cm and 4 cm; height 4 cm
  2. 2Area = (10 + 4)/2 × 4
  3. 3= 28 cm²

Answer28 cm²

Part (aii) · 1 mark

Measure the size of angle w in quadrilateral B.

  1. 1Place the protractor at the vertex (2, 6) and read the angle: w = 117°

Answer117

Part (aiiia) · 3 marks

Describe fully the single transformation taking quadrilateral A onto quadrilateral B.

  1. 1Sides of B are twice those of A, so scale factor = 2
  2. 2Lines through corresponding vertices, e.g. (3, 4) to (4, 10) and (2, 2) to (2, 6), meet at (2, −2)
  3. 3Enlargement, centre (2, −2), scale factor 2

AnswerEnlargement, centre (2, −2), scale factor 2

Part (aiiib) · 3 marks

Describe fully the single transformation taking quadrilateral A onto quadrilateral C.

  1. 1(−2, 4) stays fixed, so it is the centre
  2. 2(3, 4) → (−2, −1): the vector (5, 0) turns to (0, −5)
  3. 3Rotation, centre (−2, 4), 90° clockwise

AnswerRotation, centre (−2, 4), 90° clockwise

Part (b) · 2 marks

On the grid, complete triangle ABC using line AB so its area equals the parallelogram's area.

  1. 1Area of parallelogram = 9 × 2 = 18 cm²
  2. 2Triangle: 1/2 × 6 × h = 18, so h = 6 cm
  3. 3Mark C anywhere 6 cm (6 squares) from line AB and join it to A and B

AnswerA correct triangle drawn

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Also searched as: 0580/32/F/M/22 · 0580_m22_qp_32 · 0580 m22 32 · question 3.
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