Primary 6 PSLE Mathematics Area Perimeter Quiz

Answer Key - Primary 6 PSLE Mathematics Quiz - Area Perimeter

Total Marks: 50

Section A: Multiple-Choice Questions (10 marks)

1. B) 40 cm

• Marks: 2
• Working: Perimeter of rectangle = 2 × (length + width) = 2 × (12 + 8) = 2 × 20 = 40 cm.
• Explanation: The perimeter is the total distance around the outside of the rectangle. We add the length and width, then multiply by 2 because there are two lengths and two widths.
• Common mistake: Option D (40 cm²) uses area units (cm²) instead of perimeter units (cm). Option C (96 cm²) is the area (12 × 8).

2. B) 8 cm

• Marks: 2
• Working: Area of square = side × side = side². So side = √(area) = √64 = 8 cm.
• Explanation: The area of a square is found by multiplying the side length by itself. To find the side from the area, we take the square root.
• Common mistake: Option A (4 cm) is half of 8. Option C (16 cm) is 2 × 8. Option D (32 cm) is 4 × 8.

3. B) 30 cm²

• Marks: 2
• Working: Area of triangle = ½ × base × height = ½ × 10 × 6 = 30 cm².
• Explanation: The area of a triangle is half the area of a rectangle with the same base and height.
• Common mistake: Option C (60 cm²) forgets to multiply by ½. Option D (30 cm) uses length units instead of area units.

4. B) 49.98 cm

• Marks: 2
• Working: Perimeter = perimeter of rectangle (excluding the top side) + circumference of semicircle.
  • Rectangle: 2 × (14 + 7) = 42 cm. But the top side (14 cm) is replaced by the semicircle, so we subtract it: 42 - 14 = 28 cm.
  • Semicircle circumference = ½ × π × d = ½ × 3.14 × 14 = 21.98 cm.
  • Total perimeter = 28 + 21.98 = 49.98 cm.
• Explanation: The perimeter of a composite figure is the total distance around its outer boundary. The semicircle replaces the top side of the rectangle, so we don't count that side.
• Common mistake: Option A (35.98 cm) forgets to add the rectangle's sides. Option C (63.98 cm) adds the full circle circumference instead of half.

5. D) 120 cm²

• Marks: 2
• Working: Area of parallelogram = base × height = 15 × 8 = 120 cm².
• Explanation: The area of a parallelogram is found the same way as a rectangle: base times perpendicular height.
• Common mistake: Option C (60 cm²) uses ½ × base × height (triangle formula).

Section B: Short-Answer Questions (20 marks)

6. 450 m²

• Marks: 2
• Working: Area = length × width = 25 × 18 = 450 m².
• Explanation: The area of a rectangle is found by multiplying its length by its width.
• Marking note: Award 1 mark for correct method (25 × 18), 1 mark for correct answer with units.

7. 36 cm

• Marks: 2
• Working: Length of wire = perimeter of square = 4 × side = 4 × 9 = 36 cm.
• Explanation: The wire forms the boundary of the square, so its length equals the perimeter of the square.
• Marking note: Award 1 mark for correct method, 1 mark for correct answer.

8. 10 cm

• Marks: 2
• Working: Area of triangle = ½ × base × height. So height = (2 × area) ÷ base = (2 × 45) ÷ 9 = 90 ÷ 9 = 10 cm.
• Explanation: We rearrange the triangle area formula to find the height. Multiply the area by 2 to get the area of the corresponding rectangle, then divide by the base.
• Marking note: Award 1 mark for correct rearrangement, 1 mark for correct answer.

9. 43.96 cm

• Marks: 2
• Working: Circumference = 2 × π × r = 2 × 3.14 × 7 = 43.96 cm.
• Explanation: The circumference of a circle is the distance around it. The formula is 2πr or πd.
• Marking note: Award 1 mark for correct formula, 1 mark for correct answer.

10. 10 cm

• Marks: 2
• Working: Perimeter = 2 × (length + width). So 48 = 2 × (14 + width). 14 + width = 24. Width = 24 - 14 = 10 cm.
• Explanation: We work backwards from the perimeter formula. First divide the perimeter by 2, then subtract the length to find the width.
• Marking note: Award 1 mark for correct method, 1 mark for correct answer.

11. 76 cm²

• Marks: 2
• Working: Area of square = 6 × 6 = 36 cm². Area of rectangle = 10 × 4 = 40 cm². Total area = 36 + 40 = 76 cm².
• Explanation: The total area of a composite shape is the sum of the areas of its parts.
• Marking note: Award 1 mark for finding both areas correctly, 1 mark for correct total.

12. 76.93 cm²

• Marks: 2
• Working: Radius = diameter ÷ 2 = 14 ÷ 2 = 7 cm. Area of semicircle = ½ × π × r² = ½ × 3.14 × 7² = ½ × 3.14 × 49 = 76.93 cm².
• Explanation: A semicircle is half of a circle. First find the radius, then calculate the area of the full circle, then divide by 2.
• Marking note: Award 1 mark for correct radius and formula, 1 mark for correct answer.

13. 536 cm²

• Marks: 2
• Working: Area of paper = 30 × 20 = 600 cm². Area of square cut out = 8 × 8 = 64 cm². Remaining area = 600 - 64 = 536 cm².
• Explanation: When a shape is cut out from another shape, the remaining area is the original area minus the area of the cut-out piece.
• Marking note: Award 1 mark for finding both areas, 1 mark for correct subtraction.

14. 10 cm

• Marks: 2
• Working: Circumference = 2 × π × r. So r = circumference ÷ (2 × π) = 62.8 ÷ (2 × 3.14) = 62.8 ÷ 6.28 = 10 cm.
• Explanation: We rearrange the circumference formula to find the radius. Divide the circumference by 2π.
• Marking note: Award 1 mark for correct rearrangement, 1 mark for correct answer.

15. 50 cm²

• Marks: 2
• Working: Area of trapezium = ½ × (sum of parallel sides) × height = ½ × (8 + 12) × 5 = ½ × 20 × 5 = 50 cm².
• Explanation: The area of a trapezium is found by averaging the lengths of the parallel sides and multiplying by the height.
• Marking note: Award 1 mark for correct formula, 1 mark for correct answer.

Section C: Problem-Solving Questions (20 marks)

16. 384 m²

• Marks: 4
• Working:
  • Area of field = 60 × 40 = 2400 m².
  • Inner rectangle length = 60 - 2 - 2 = 56 m.
  • Inner rectangle width = 40 - 2 - 2 = 36 m.
  • Area of inner rectangle = 56 × 36 = 2016 m².
  • Area of path = 2400 - 2016 = 384 m².
• Explanation: The path runs inside the boundary, so we subtract 2 m from each side of the field to find the inner rectangle dimensions. The path area is the difference between the outer and inner areas.
• Marking scheme:
  • 1 mark: Correct area of field.
  • 1 mark: Correct inner dimensions (56 m and 36 m).
  • 1 mark: Correct area of inner rectangle.
  • 1 mark: Correct final answer.
• Common mistake: Subtracting 2 m only once from each dimension (giving 58 m and 38 m). Remember the path is on both sides, so subtract 2 m twice.

17. 8 cm

• Marks: 4
• Working:
  • Length of wire = perimeter of square = 4 × 12 = 48 cm.
  • Perimeter of rectangle = 2 × (length + width) = 48 cm.
  • 2 × (16 + width) = 48.
  • 16 + width = 24.
  • Width = 24 - 16 = 8 cm.
• Explanation: The wire's length doesn't change when it's rebent. So the perimeter of the square equals the perimeter of the rectangle. We then work backwards to find the width.
• Marking scheme:
  • 1 mark: Correct perimeter of square.
  • 1 mark: Setting up the equation.
  • 1 mark: Correct working.
  • 1 mark: Correct final answer.
• Common mistake: Forgetting that the perimeter is the total length of wire, not the area.

18. 433.86 cm²

• Marks: 4
• Working:
  • Area of rectangle = 20 × 14 = 280 cm².
  • Radius of each semicircle = 14 ÷ 2 = 7 cm.
  • Area of one full circle = π × r² = 3.14 × 7² = 3.14 × 49 = 153.86 cm².
  • Area of two semicircles = area of one full circle = 153.86 cm².
  • Total area = 280 + 153.86 = 433.86 cm².
• Explanation: Two semicircles with the same diameter make one full circle. So we calculate the area of the rectangle and add the area of one full circle.
• Marking scheme:
  • 1 mark: Correct area of rectangle.
  • 1 mark: Correct radius.
  • 1 mark: Correct area of circle.
  • 1 mark: Correct total area.
• Common mistake: Calculating the area of one semicircle and forgetting to double it.

19. 25.67 cm (or 25.7 cm)

• Marks: 4
• Working:
  • Volume of water = 50 × 30 × 25 = 37,500 cm³.
  • Volume of cube = 10 × 10 × 10 = 1,000 cm³.
  • Total volume of water + cube = 37,500 + 1,000 = 38,500 cm³.
  • Base area of tank = 50 × 30 = 1,500 cm².
  • New height = total volume ÷ base area = 38,500 ÷ 1,500 = 25.67 cm (or 25.7 cm).
• Explanation: When the cube is placed in the water, it displaces its own volume of water. The water level rises because the same amount of water now occupies a smaller space (the tank minus the cube's volume). The new height is found by dividing the total volume (water + cube) by the base area.
• Marking scheme:
  • 1 mark: Correct volume of water.
  • 1 mark: Correct volume of cube.
  • 1 mark: Correct total volume.
  • 1 mark: Correct new height.
• Common mistake: Adding the cube's volume to the water's volume but forgetting that the cube also takes up space in the tank.

20. 21.5 m²

• Marks: 4
• Working:
  • Area of square = 10 × 10 = 100 m².
  • Area of quarter circle = ¼ × π × r² = ¼ × 3.14 × 10² = ¼ × 3.14 × 100 = 78.5 m².
  • Area of shaded region = 100 - 78.5 = 21.5 m².
• Explanation: The shaded region is the part of the square not covered by the quarter circle. So we subtract the area of the quarter circle from the area of the square.
• Marking scheme:
  • 1 mark: Correct area of square.
  • 1 mark: Correct formula for quarter circle.
  • 1 mark: Correct area of quarter circle.
  • 1 mark: Correct final answer.
• Common mistake: Using the formula for a full circle instead of a quarter circle. Remember a quarter circle is ¼ of a full circle.

END OF ANSWER KEY