Lemmara logoLemmaraWorked solution

4MA1/1H Nov 2021, Question 14: Area Factor of Similar Shapes

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 8 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

For two regular hexagons centred at O with GHIJKL a scale factor 2 enlargement of ABCDEF, vectors OA = a and OB = b, find given vectors and the shaded region's area.

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

Part (ai) · 1 mark

Express vector AB in terms of a and b, simplified.

  1. 1AB = OB − OA
  2. 2AB = b − a

Answerb − a

Part (aii) · 2 marks

Express vector KI in terms of a and b, simplified.

  1. 1K is the image of E and I the image of C, so OK = −2b and OI = 2(b − a)
  2. 2KI = OI − OK = 2b − 2a + 2b
  3. 3KI = 4b − 2a

Answer4b − 2a

Part (aiii) · 2 marks

Express vector LD in terms of a and b, simplified.

  1. 1L is the image of F, so OL = 2(a − b), and OD = −a
  2. 2LD = OD − OL = −a − 2a + 2b
  3. 3LD = 2b − 3a

Answer2b − 3a

Part (b) · 3 marks

Given triangle OAB has area 5 cm², calculate the area of the shaded region between the hexagons.

  1. 1Area of small hexagon ABCDEF = 6 × area of triangle OAB = 6 × 5 = 30 cm²
  2. 2GHIJKL is enlargement of ABCDEF with scale factor 2, so area scale factor = 2² = 4
  3. 3Area of large hexagon GHIJKL = 4 × 30 = 120 cm²
  4. 4Shaded area = area of large hexagon − area of small hexagon
  5. 5Shaded area = 120 − 30 = 90 cm²

Answer90

Stuck on a step? Read the free lesson: Area Factor of Similar Shapes

Practise more area factor of similar shapes questions

Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on area factor of similar shapes

Also searched as: 4MA1 1H November 2021 · 4MA1/1H · 4ma1 nov21 1h · question 14.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.