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4MA1/2FR Jun 2019, Question 10: Angles in a Quadrilateral

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2FR (Foundation) · Calculator · 4 marks

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The question, in short

Use kite properties to find the marked angle x in ABCD, then calculate the area of kite PQRS from its given side lengths and right angle.

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

Part (a) · 2 marks

Find the size of angle BAD, marked x, in kite ABCD using its equal sides and given angles.

  1. 1In a kite, angle ADC = angle ABC = 90°
  2. 2Angles in a quadrilateral add to 360°
  3. 3x = 360 − (90 + 90 + 140)
  4. 4x = 40°

Answer40

Part (b) · 2 marks

Calculate the area of kite PQRS using PQ = 33 cm, QR = 12 cm and angle PQR = 90°.

  1. 1The kite is two identical right-angled triangles
  2. 2One triangle: 1/2 × 33 × 12 = 198
  3. 3Area = 2 × 198 = 396 cm²

Answer396

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