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4MA1/1F Jun 2023, Question 13: Perimeter and Area of a Rectangle

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 5 marks

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The question, in short

Use the equal perimeters of a 5 cm high rectangle and an isosceles triangle with sides 8 cm and base 12 cm, then find the rectangle's area and a cuboid's missing width w given volume 231 cm³.

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Part (a) · 3 marks

Find the area of the rectangle, given its height is 5 cm and its perimeter equals that of the triangle with equal sides 8 cm and base 12 cm.

  1. 1Triangle perimeter = 8 + 8 + 12 = 28 cm
  2. 2Rectangle: 2 × length + 2 × 5 = 28, so 2 × length = 18
  3. 3Length = 18 ÷ 2 = 9 cm
  4. 4Area = 9 × 5 = 45

Answer45

Part (b) · 2 marks

Calculate w for a cuboid measuring 7 cm by w cm by 6 cm whose volume is 231 cm³.

  1. 1Volume of a cuboid = length × width × height
  2. 27 × 6 × w = 231, so 42w = 231
  3. 3w = 231 ÷ 42 = 5.5

Answer5.5

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