Primary 4 Mathematics Area Perimeter Quiz

Primary 4 Mathematics Quiz - Area Perimeter: Answer Key

Total Marks: 40

Section A: Multiple Choice Questions (Questions 1 to 5)

1. Answer: B) 40 cm (1 mark)

• Working: Perimeter of a rectangle = 2 × (length + width) = 2 × (12 cm + 8 cm) = 2 × 20 cm = 40 cm.
• Teaching Note: Perimeter is the total distance around the outside of a shape. For a rectangle, opposite sides are equal, so we add the length and width and multiply by 2.
• Common Mistake: Some students may calculate area (12 × 8 = 96 cm²) instead of perimeter. Remember: perimeter is the distance around, area is the space inside.

2. Answer: C) 9 cm (1 mark)

• Working: A square has 4 equal sides. Side length = Perimeter ÷ 4 = 36 cm ÷ 4 = 9 cm.
• Teaching Note: Since all sides of a square are equal, we divide the total perimeter by 4 to find the length of one side.
• Common Mistake: Some students may divide by 2 instead of 4. Remember a square has 4 sides.

3. Answer: B) 8 cm (1 mark)

• Working: Area of a rectangle = length × width. So, width = Area ÷ length = 72 cm² ÷ 9 cm = 8 cm.
• Teaching Note: If we know the area and one side of a rectangle, we can find the other side by dividing the area by the known side.
• Common Mistake: Some students may subtract instead of divide. Remember: area is found by multiplication, so the reverse operation is division.

4. Answer: D) A square of side 6 cm (1 mark)

• Working:
  • A) Area = 5 cm × 5 cm = 25 cm²
  • B) Area = 6 cm × 4 cm = 24 cm²
  • C) Area = 7 cm × 3 cm = 21 cm²
  • D) Area = 6 cm × 6 cm = 36 cm²
  • The largest area is 36 cm² (square of side 6 cm).
• Teaching Note: To compare areas, calculate each area and compare the numbers. A square of side 6 cm has a larger area than the other options.

5. Answer: B) 46 m² (1 mark)

• Working:
  • Area of garden including path = 15 m × 10 m = 150 m²
  • Area of garden without path = (15 m - 2 m) × (10 m - 2 m) = 13 m × 8 m = 104 m²
  • Area of path = 150 m² - 104 m² = 46 m²
• Teaching Note: The path runs inside the garden, so the inner rectangle is smaller by 2 m in each dimension (1 m on each side). Subtract the inner area from the outer area to find the path area.
• Common Mistake: Some students forget to subtract the path width from both sides, so they subtract only 1 m instead of 2 m from each dimension.

Section B: Short Answer Questions (Questions 6 to 15)

6. Answer: 126 cm² (2 marks: 1 mark for correct working, 1 mark for correct answer)

• Working: Area = length × width = 14 cm × 9 cm = 126 cm².
• Teaching Note: Area measures the space inside a shape. For a rectangle, multiply the length by the width. Remember to write the units as cm² (square centimetres).

7. Answer: 32 cm (2 marks: 1 mark for finding side length, 1 mark for correct perimeter)

• Working:
  • Side length = √Area = √64 cm² = 8 cm (since 8 × 8 = 64)
  • Perimeter = 4 × side = 4 × 8 cm = 32 cm.
• Teaching Note: First find the side length by finding the square root of the area (what number multiplied by itself gives 64?). Then multiply the side length by 4 to find the perimeter.
• Common Mistake: Some students may think the side length is 64 ÷ 4 = 16 cm. Remember: area of a square is side × side, not side × 4.

8. Answer: 9 cm (2 marks: 1 mark for correct working, 1 mark for correct answer)

• Working:
  • Perimeter = 2 × (length + width)
  • 48 cm = 2 × (15 cm + width)
  • 15 cm + width = 48 cm ÷ 2 = 24 cm
  • width = 24 cm - 15 cm = 9 cm.
• Teaching Note: Work backwards from the perimeter formula. First divide the perimeter by 2 to find the sum of length and width, then subtract the known length to find the width.

9. Answer: 216 cm² (2 marks: 1 mark for correct working, 1 mark for correct answer)

• Working: Area = length × width = 18 cm × 12 cm = 216 cm².
• Teaching Note: Direct application of the area formula for a rectangle. Multiply the given length and width.

10. Answer: 82 m (2 marks: 1 mark for correct working, 1 mark for correct answer)

• Working: Perimeter = 2 × (length + width) = 2 × (25 m + 16 m) = 2 × 41 m = 82 m.
• Teaching Note: Direct application of the perimeter formula. Add the length and width, then multiply by 2.

11. Answer: 225 cm² (2 marks: 1 mark for finding side length, 1 mark for correct area)

• Working:
  • Side length = Perimeter ÷ 4 = 60 cm ÷ 4 = 15 cm
  • Area = side × side = 15 cm × 15 cm = 225 cm².
• Teaching Note: First find the side length from the perimeter, then use the side length to find the area.

12. Answer: 12 cm (2 marks: 1 mark for correct working, 1 mark for correct answer)

• Working: Length = Area ÷ width = 108 cm² ÷ 9 cm = 12 cm.
• Teaching Note: If we know the area and width, divide the area by the width to find the length.

13. Answer: 575 m² (2 marks: 1 mark for finding areas, 1 mark for correct subtraction)

• Working:
  • Area of field = 30 m × 20 m = 600 m²
  • Area of pond = 5 m × 5 m = 25 m²
  • Area not covered = 600 m² - 25 m² = 575 m².
• Teaching Note: Find the area of the whole field, then subtract the area of the pond. The pond is a square, so its area is side × side.

14. Answer: 18 cm (2 marks: 1 mark for correct working, 1 mark for correct answer)

• Working:
  • Perimeter = 2 × (length + width)
  • 56 cm = 2 × (length + 10 cm)
  • length + 10 cm = 56 cm ÷ 2 = 28 cm
  • length = 28 cm - 10 cm = 18 cm.
• Teaching Note: Work backwards from the perimeter formula. Divide the perimeter by 2, then subtract the known width.

15. Answer: 84 cm (2 marks: 1 mark for understanding the shape, 1 mark for correct perimeter)

• Working:
  • Original perimeter = 2 × (24 cm + 18 cm) = 84 cm
  • Cutting squares from corners does not change the perimeter of the remaining shape because the cut edges are replaced by new edges of the same total length.
  • The perimeter remains 84 cm.
• Teaching Note: When you cut a square from each corner of a rectangle, the perimeter of the remaining shape is the same as the original rectangle. The cut-out parts are replaced by new edges of equal length. This is a common problem type in P4 exams.
• Marking Note: Award 1 mark for understanding that the perimeter does not change, and 1 mark for the correct answer.

Section C: Problem-Solving Questions (Questions 16 to 20)

16. Answer: 78 m² (3 marks: 1 mark for outer area, 1 mark for inner area, 1 mark for correct subtraction)

• Working:
  • Outer rectangle (pool + border): length = 25 m + 2 m = 27 m, width = 12 m + 2 m = 14 m
  • Area of outer rectangle = 27 m × 14 m = 378 m²
  • Area of pool = 25 m × 12 m = 300 m²
  • Area of border = 378 m² - 300 m² = 78 m².
• Teaching Note: The border is outside the pool, so the outer rectangle is larger by 1 m on each side (2 m total in each dimension). Calculate the area of the outer rectangle, subtract the area of the pool to find the border area.
• Common Mistake: Some students forget to add the border width to both sides of the pool. Remember: if the border is 1 m wide, the outer rectangle is 2 m longer and 2 m wider than the pool.

17. Answer: 2 m (3 marks: 1 mark for setting up equation, 1 mark for correct working, 1 mark for correct answer)

• Working:
  • Let the width of the path be x m.
  • Inner rectangle dimensions: length = 40 - 2x, width = 30 - 2x
  • Area of path = Area of outer - Area of inner
  • 216 = (40 × 30) - [(40 - 2x)(30 - 2x)]
  • 216 = 1200 - (1200 - 80x - 60x + 4x²)
  • 216 = 1200 - 1200 + 140x - 4x²
  • 216 = 140x - 4x²
  • 4x² - 140x + 216 = 0
  • Divide by 4: x² - 35x + 54 = 0
  • (x - 2)(x - 27) = 0
  • x = 2 or x = 27
  • Since the path width cannot be 27 m (larger than the land), x = 2 m.
• Teaching Note: This is a challenging problem. Set up an equation where the area of the path equals the difference between the outer and inner areas. The inner rectangle dimensions are reduced by 2x (x on each side). Solve the quadratic equation to find x.
• Marking Note: Award 1 mark for correct setup, 1 mark for correct equation and solving, 1 mark for selecting the correct answer (2 m).

18. Answer: 192 cm² (3 marks: 1 mark for finding width, 1 mark for finding length, 1 mark for correct area)

• Working:
  • Let the width be w cm. Then the length is 3w cm.
  • Perimeter = 2 × (length + width) = 2 × (3w + w) = 2 × 4w = 8w
  • 8w = 64 cm
  • w = 64 ÷ 8 = 8 cm (width)
  • Length = 3 × 8 cm = 24 cm
  • Area = length × width = 24 cm × 8 cm = 192 cm².
• Teaching Note: Use a variable to represent the unknown width. Express the length in terms of the width, then use the perimeter formula to find the width. Once you have both dimensions, calculate the area.
• Common Mistake: Some students may forget that the length is 3 times the width, not 3 cm more.

19. Answer: 124 m² (3 marks: 1 mark for outer area, 1 mark for inner area, 1 mark for correct subtraction)

• Working:
  • Outer rectangle (garden): length = 20 m, width = 15 m
  • Area of garden = 20 m × 15 m = 300 m²
  • Inner rectangle (garden without flower bed): length = 20 m - 4 m = 16 m, width = 15 m - 4 m = 11 m
  • Area of inner rectangle = 16 m × 11 m = 176 m²
  • Area of flower bed = 300 m² - 176 m² = 124 m².
• Teaching Note: The flower bed runs along the inside of the garden, so the inner rectangle is smaller by 2 × width of flower bed in each dimension (2 m on each side, so 4 m total). Subtract the inner area from the outer area.
• Common Mistake: Some students may subtract only 2 m from each dimension instead of 4 m. Remember: the flower bed is 2 m wide on each side, so the inner rectangle is 4 m shorter in both length and width.

20. Answer: 144 cm² (3 marks: 1 mark for finding side of square, 1 mark for correct working, 1 mark for correct area)

• Working:
  • Let the side of the original square be s cm.
  • When folded in half, the rectangle has dimensions: length = s cm, width = s/2 cm.
  • Perimeter of rectangle = 2 × (s + s/2) = 2 × (3s/2) = 3s
  • 3s = 36 cm
  • s = 12 cm (side of original square)
  • Area of original square = 12 cm × 12 cm = 144 cm².
• Teaching Note: When a square is folded in half, the resulting rectangle has the same length as the square's side, but half the width. Use the perimeter of the rectangle to find the side of the square, then calculate the area.
• Common Mistake: Some students may think the rectangle's dimensions are s/2 and s/2, forgetting that the length remains the same as the square's side.

End of Answer Key