Primary 5 Mathematics Area Perimeter Quiz

Primary 5 Mathematics Quiz - Area Perimeter (Answer Key)

General Note:

• Units must be included in the final answer.
• Working must be shown for Section B and C to earn method marks.
• $\text{Area of Rectangle} = \text{Length} \times \text{Breadth}$
• $\text{Perimeter of Rectangle} = 2 \times (\text{Length} + \text{Breadth})$
• $\text{Area of Square} = \text{Side} \times \text{Side}$
• $\text{Perimeter of Square} = 4 \times \text{Side}$
• $\text{Area of Triangle} = \frac{1}{2} \times \text{Base} \times \text{Height}$

Section A: Multiple Choice Questions

1. (3)

• Reasoning:
  • $\text{Area} = \text{Length} \times \text{Breadth} \Rightarrow 48 = 8 \times \text{Breadth}$.
  • $\text{Breadth} = 48 \div 8 = 6 \text{ cm}$.
  • $\text{Perimeter} = 2 \times (8 + 6) = 2 \times 14 = 28 \text{ cm}$.
• Common Mistake: Adding length and breadth only ($8+6=14$) or forgetting to multiply by 2.

2. (3)

• Reasoning:
  • $\text{Perimeter} = 4 \times \text{Side} \Rightarrow 36 = 4 \times \text{Side}$.
  • $\text{Side} = 36 \div 4 = 9 \text{ m}$.
  • $\text{Area} = 9 \times 9 = 81 \text{ m}^2$.
• Common Mistake: Confusing perimeter formula with area, or squaring the perimeter.

3. (1)

• Reasoning:
  • Let the side of the square be $10 \text{ cm}$.
  • If they did not overlap, total width would be $10 + 10 = 20 \text{ cm}$.
  • Actual width is $15 \text{ cm}$.
  • $\text{Overlap length} = 20 - 15 = 5 \text{ cm}$.
  • Since they are squares, the overlap is a square of side $5 \text{ cm}$.
  • $\text{Area of overlap} = 5 \times 5 = 25 \text{ cm}^2$.
• Visual Check: The diagram shows the total span is less than the sum of individual widths. The difference is the shared region.

4. (2)

• Reasoning:
  • $\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}$.
  • $\text{Area} = \frac{1}{2} \times 12 \times 5 = 6 \times 5 = 30 \text{ cm}^2$.
• Common Mistake: Forgetting the $\frac{1}{2}$, resulting in $60$.

5. (2)

• Reasoning:
  • $\text{Perimeter} = 2 \times (\text{Length} + \text{Breadth})$.
  • $50 = 2 \times (15 + \text{Breadth})$.
  • $25 = 15 + \text{Breadth}$.
  • $\text{Breadth} = 25 - 15 = 10 \text{ cm}$.

Section B: Short Answer Questions

6. $63 \text{ cm}^2$

• Working:
  • $\text{Area} = \frac{1}{2} \times 14 \times 9$
  • $= 7 \times 9$
  • $= 63 \text{ cm}^2$

7. $40 \text{ m}$

• Working:
  • $\text{Perimeter} = 2 \times (12 + 8)$
  • $= 2 \times 20$
  • $= 40 \text{ m}$

8. $12 \text{ cm}$

• Working:
  • $\text{Area} = \text{Side} \times \text{Side} = 144$.
  • $\sqrt{144} = 12$.
  • Side $= 12 \text{ cm}$.

9. $215 \text{ cm}^2$

• Working:
  • $\text{Area of original rectangle} = 20 \times 12 = 240 \text{ cm}^2$.
  • $\text{Area of cut-out square} = 5 \times 5 = 25 \text{ cm}^2$.
  • $\text{Remaining Area} = 240 - 25 = 215 \text{ cm}^2$.
• Note: Cutting a corner does not change the perimeter, but it does reduce the area.

10. $72 \text{ cm}^2$

• Working:
  • Method 1 (Split into two rectangles):
    • Rectangle A (vertical part excluding overlap with B's height? No, standard L-shape split):
    • Let's split vertically: Left rectangle is $4 \text{ cm}$ wide and $10 \text{ cm}$ high. Area $= 40 \text{ cm}^2$.
    • Right rectangle is remaining width. Total width is not explicitly given as sum, but diagram labels imply:
    • Actually, looking at Q10 placeholder: Width A=4, Height A=10. Width B=8, Height B=4.
    • Usually, L-shapes are joined. If joined at bottom-right of A and top-left of B?
    • Let's assume standard non-overlapping composition based on "Total width 12" in placeholder description vs "Width A 4, Width B 8". $4+8=12$. So they are side-by-side horizontally? No, "L-shaped".
    • Correct interpretation of L-shape from placeholder: Vertical bar (4x10) and Horizontal bar (8x4). If they form an L, they share a corner or side.
    • Let's assume the standard decomposition:
      • Vertical Rectangle: $4 \text{ cm} \times 10 \text{ cm} = 40 \text{ cm}^2$.
      • Horizontal Rectangle (extending from bottom): The placeholder says Width B=8. If it's an L, the total width is usually $4+8=12$? Or is B the entire bottom?
      • Let's use the explicit values: Area A $= 4 \times 10 = 40$. Area B $= 8 \times 4 = 32$.
      • If they are distinct parts of the L (non-overlapping), Total Area $= 40 + 32 = 72 \text{ cm}^2$.
• Answer: $72 \text{ cm}^2$.

11. $9 \text{ cm}$

• Working:
  • Equilateral triangle has 3 equal sides.
  • $\text{Side} = \text{Perimeter} \div 3$
  • $= 27 \div 3 = 9 \text{ cm}$.

12. $20 \text{ m}$

• Working:
  • $\text{Area} = \text{Length} \times \text{Breadth}$
  • $200 = \text{Length} \times 10$
  • $\text{Length} = 200 \div 10 = 20 \text{ m}$.

13. $84 \text{ cm}^2$

• Working:
  • $\text{Area of large rectangle} = 15 \times 10 = 150 \text{ cm}^2$.
  • $\text{Area of small rectangle} = 11 \times 6 = 66 \text{ cm}^2$.
  • $\text{Shaded Area} = 150 - 66 = 84 \text{ cm}^2$.

14. $4 \text{ cm}$

• Working:
  • $\text{Perimeter of square} = 4 \times 6 = 24 \text{ cm}$.
  • $\text{Perimeter of rectangle} = 24 \text{ cm}$.
  • $2 \times (8 + \text{Breadth}) = 24$.
  • $8 + \text{Breadth} = 12$.
  • $\text{Breadth} = 12 - 8 = 4 \text{ cm}$.

15. $10 \text{ cm}$

• Working:
  • $\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}$
  • $80 = \frac{1}{2} \times 16 \times \text{Height}$
  • $80 = 8 \times \text{Height}$
  • $\text{Height} = 80 \div 8 = 10 \text{ cm}$.

Section C: Long Answer Questions

16. (a) $100 \text{ cm}^2$

• Working:
  • $\text{Area of square} = \text{Side} \times \text{Side}$
  • $= 10 \times 10 = 100 \text{ cm}^2$.

(b) $140 \text{ cm}^2$

• Working:
  • $\text{Area of triangle} = \frac{1}{2} \times \text{Base} \times \text{Height}$
  • Base of triangle = Side of square $= 10 \text{ cm}$.
  • $\text{Area} = \frac{1}{2} \times 10 \times 8 = 40 \text{ cm}^2$.
  • $\text{Total Area} = \text{Area of Square} + \text{Area of Triangle}$
  • $= 100 + 40 = 140 \text{ cm}^2$.

17. (a) $48 \text{ m}^2$

• Working:
  • $\text{Area} = 8 \text{ m} \times 6 \text{ m} = 48 \text{ m}^2$.

(b) 192 tiles

• Working:
  • Convert units to be consistent. Let's use cm.
  • $\text{Room Area} = 48 \text{ m}^2 = 48 \times 10,000 \text{ cm}^2 = 480,000 \text{ cm}^2$.
  • $\text{Tile Side} = 50 \text{ cm}$.
  • $\text{Tile Area} = 50 \times 50 = 2,500 \text{ cm}^2$.
  • $\text{Number of tiles} = 480,000 \div 2,500$.
  • $4800 \div 25 = 192$.
  • Alternative Method:
    • Length in tiles: $8 \text{ m} = 800 \text{ cm}$. $800 \div 50 = 16$ tiles.
    • Breadth in tiles: $6 \text{ m} = 600 \text{ cm}$. $600 \div 50 = 12$ tiles.
    • $\text{Total tiles} = 16 \times 12 = 192$.

18. (a) $40 \text{ cm}^2$

• Working:
  • Rectangle $ABFE$:
  • $\text{Length } AB = 10 \text{ cm}$.
  • $\text{Breadth } AE = 4 \text{ cm}$.
  • $\text{Area} = 10 \times 4 = 40 \text{ cm}^2$.

(b) $36 \text{ cm}$

• Working:
  • Rectangle $EFCD$:
  • $\text{Height } EF = AB = 10 \text{ cm}$.
  • $\text{Width } ED = AD - AE = 12 - 4 = 8 \text{ cm}$.
  • $\text{Perimeter} = 2 \times (10 + 8) = 2 \times 18 = 36 \text{ cm}$.

19. (a) $10 \text{ cm}$

• Working:
  • Let Breadth $= u$.
  • Then Length $= 2u$.
  • $\text{Perimeter} = 2 \times (\text{Length} + \text{Breadth})$.
  • $60 = 2 \times (2u + u)$.
  • $60 = 2 \times 3u$.
  • $60 = 6u$.
  • $u = 10$.
  • Breadth $= 10 \text{ cm}$.

(b) $200 \text{ cm}^2$

• Working:
  • $\text{Length} = 2 \times 10 = 20 \text{ cm}$.
  • $\text{Area} = 20 \times 10 = 200 \text{ cm}^2$.

20. (a) 8 sides

• Reasoning:
  • When 3 squares are in a row, the internal touching sides are not part of the perimeter.
  • Top: 3 sides.
  • Bottom: 3 sides.
  • Left end: 1 side.
  • Right end: 1 side.
  • Total $= 3 + 3 + 1 + 1 = 8$ sides.

(b) $36 \text{ cm}^2$

• Working:
  • $\text{Perimeter} = 8 \times \text{Side of small square}$.
  • $48 = 8 \times \text{Side}$.
  • $\text{Side} = 48 \div 8 = 6 \text{ cm}$.
  • $\text{Area of one small square} = 6 \times 6 = 36 \text{ cm}^2$.

(c) $108 \text{ cm}^2$

• Working:
  • $\text{Total Area} = 3 \times \text{Area of one small square}$.
  • $= 3 \times 36 = 108 \text{ cm}^2$.
  • Check: Total shape is $18 \text{ cm}$ by $6 \text{ cm}$. $18 \times 6 = 108 \text{ cm}^2$. Correct.