Primary 5 Mathematics Area Perimeter Quiz

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Primary 5 Mathematics Quiz - Area Perimeter

Name: __________________________
Class: __________________________
Date: __________________________
Score: _________ / 40

Duration: 1 hour 15 minutes
Total Marks: 40

Instructions to Candidates:

1. This quiz consists of 20 questions.
2. Answer all questions.
3. Write your answers in the spaces provided.
4. For questions requiring working, show your working clearly. Marks may be awarded for method even if the final answer is incorrect.
5. Unless otherwise stated, give your answers in the simplest form.
6. Use $\pi = \frac{22}{7}$ or $3.14$ where appropriate (though this topic focuses on rectilinear shapes, triangles, and composite figures).

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

Each question carries 1 mark. Choose the correct answer and write its number (1, 2, 3, or 4) in the brackets provided.

1. The area of a rectangle is $48 \text{ cm}^2$. If its length is $8 \text{ cm}$, what is its perimeter? (1) $14 \text{ cm}$ (2) $20 \text{ cm}$ (3) $28 \text{ cm}$ (4) $56 \text{ cm}$

Answer: ( ______ )

2. A square has a perimeter of $36 \text{ m}$. What is its area? (1) $9 \text{ m}^2$ (2) $18 \text{ m}^2$ (3) $81 \text{ m}^2$ (4) $144 \text{ m}^2$

Answer: ( ______ )

3. The figure below shows two identical squares overlapping. <image_placeholder> id: Q3-fig1 type: diagram linked_question: Q3 description: Two identical squares of side 10 cm overlapping. The overlap is a smaller square in the center. The total width of the combined shape is 15 cm. labels: Side of large square = 10 cm, Total width = 15 cm values: Side = 10, Total Width = 15 must_show: The overlapping region, dimensions labeled clearly. </image_placeholder> What is the area of the overlapping region? (1) $25 \text{ cm}^2$ (2) $50 \text{ cm}^2$ (3) $75 \text{ cm}^2$ (4) $100 \text{ cm}^2$

Answer: ( ______ )

4. A triangle has a base of $12 \text{ cm}$ and a height of $5 \text{ cm}$. What is its area? (1) $17 \text{ cm}^2$ (2) $30 \text{ cm}^2$ (3) $60 \text{ cm}^2$ (4) $120 \text{ cm}^2$

Answer: ( ______ )

5. The perimeter of a rectangle is $50 \text{ cm}$. If the length is $15 \text{ cm}$, what is the breadth? (1) $5 \text{ cm}$ (2) $10 \text{ cm}$ (3) $20 \text{ cm}$ (4) $35 \text{ cm}$

Answer: ( ______ )

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

Each question carries 2 marks. Show your working.

6. Find the area of a triangle with a base of $14 \text{ cm}$ and a height of $9 \text{ cm}$.

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Answer: _______________ $\text{cm}^2$

7. A rectangular garden is $12 \text{ m}$ long and $8 \text{ m}$ wide. A fence is built around the garden. Find the length of the fence.

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Answer: _______________ $\text{m}$

8. The area of a square is $144 \text{ cm}^2$. Find the length of one side of the square.

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Answer: _______________ $\text{cm}$

9. A rectangle has a length of $20 \text{ cm}$ and a breadth of $12 \text{ cm}$. A square of side $5 \text{ cm}$ is cut out from one corner. What is the area of the remaining shape?

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Answer: _______________ $\text{cm}^2$

10. The figure below is made up of two rectangles, A and B. <image_placeholder> id: Q10-fig1 type: diagram linked_question: Q10 description: An L-shaped figure composed of two rectangles. Rectangle A is vertical (width 4cm, height 10cm). Rectangle B is horizontal attached to the bottom right of A (width 8cm, height 4cm). The total height is 10cm, total width is 12cm. labels: Width of A = 4 cm, Height of A = 10 cm, Width of B = 8 cm, Height of B = 4 cm values: wA=4, hA=10, wB=8, hB=4 must_show: The L-shape, dimensions labeled on the outer edges. </image_placeholder> Find the total area of the figure.

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Answer: _______________ $\text{cm}^2$

11. The perimeter of an equilateral triangle is $27 \text{ cm}$. Find the length of one side.

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Answer: _______________ $\text{cm}$

12. A rectangular field has an area of $200 \text{ m}^2$. If its breadth is $10 \text{ m}$, find its length.

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Answer: _______________ $\text{m}$

13. The figure below shows a rectangle inside a larger rectangle. The shaded region is the area between them. <image_placeholder> id: Q13-fig1 type: diagram linked_question: Q13 description: A large rectangle (15cm by 10cm) with a smaller unshaded rectangle (11cm by 6cm) inside it. The space between is shaded. labels: Outer Length = 15 cm, Outer Breadth = 10 cm, Inner Length = 11 cm, Inner Breadth = 6 cm values: OL=15, OB=10, IL=11, IB=6 must_show: Shaded region clearly marked, dimensions of both rectangles. </image_placeholder> Find the area of the shaded region.

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Answer: _______________ $\text{cm}^2$

14. A square and a rectangle have the same perimeter. The square has a side of $6 \text{ cm}$. The rectangle has a length of $8 \text{ cm}$. Find the breadth of the rectangle.

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Answer: _______________ $\text{cm}$

15. The base of a triangle is $16 \text{ cm}$. Its area is $80 \text{ cm}^2$. Find its height.

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Answer: _______________ $\text{cm}$

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Section C: Long Answer Questions (Questions 16 – 20)

Each question carries 4 marks. Show all necessary working.

16. The figure below is made up of a square and a triangle. <image_placeholder> id: Q16-fig1 type: diagram linked_question: Q16 description: A composite shape. A square of side 10cm is at the bottom. An isosceles triangle sits on top of the square, sharing the top side of the square as its base. The height of the triangle is 8cm. labels: Square side = 10 cm, Triangle height = 8 cm values: Side=10, Height=8 must_show: The composite shape, base of triangle aligned with top of square. </image_placeholder> (a) Find the area of the square. (b) Find the total area of the figure.

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Answer: (a) _______________ $\text{cm}^2$ (b) _______________ $\text{cm}^2$

17. Mr. Tan wants to tile his rectangular living room which measures $8 \text{ m}$ by $6 \text{ m}$. Each square tile has a side of $50 \text{ cm}$. (a) What is the area of the living room in $\text{m}^2$? (b) How many tiles does he need to cover the floor completely?

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Answer: (a) _______________ $\text{m}^2$ (b) _______________ tiles

18. The figure below shows a rectangle $ABCD$. $E$ is a point on $AD$ such that $AE = 4 \text{ cm}$. $F$ is a point on $BC$ such that $BF = 4 \text{ cm}$. The length of $AB$ is $10 \text{ cm}$ and $AD$ is $12 \text{ cm}$. <image_placeholder> id: Q18-fig1 type: diagram linked_question: Q18 description: Rectangle ABCD. AB=10cm (height), AD=12cm (width). Point E on AD, 4cm from A. Point F on BC, 4cm from B. Line EF is drawn parallel to AB. The shape is divided into two smaller rectangles ABFE and EFCD. labels: AB = 10 cm, AD = 12 cm, AE = 4 cm, BF = 4 cm values: AB=10, AD=12, AE=4, BF=4 must_show: Rectangle with internal line EF, labels for all segments. </image_placeholder> (a) Find the area of rectangle $ABFE$. (b) Find the perimeter of rectangle $EFCD$.

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Answer: (a) _______________ $\text{cm}^2$ (b) _______________ $\text{cm}$

19. A piece of wire $60 \text{ cm}$ long is bent to form a rectangle. The length of the rectangle is twice its breadth. (a) Find the breadth of the rectangle. (b) Find the area of the rectangle.

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Answer: (a) _______________ $\text{cm}$ (b) _______________ $\text{cm}^2$

20. The figure below is composed of three identical squares arranged in a row. <image_placeholder> id: Q20-fig1 type: diagram linked_question: Q20 description: Three identical squares placed side-by-side horizontally to form a long rectangle. The total perimeter of the resulting shape is 48 cm. labels: Total Perimeter = 48 cm values: P_total = 48 must_show: Three squares joined, outline of the combined shape highlighted. </image_placeholder> (a) How many sides of the small squares make up the perimeter of the large shape? (b) Find the area of one small square. (c) Find the total area of the figure.

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Answer: (a) _______________ (b) _______________ $\text{cm}^2$ (c) _______________ $\text{cm}^2$

*** End of Quiz ***

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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.
• $\text{Area of Rectangle} = \text{Length} \times \text{Breadth}$
• $\text{Perimeter of Rectangle} = 2 \times (\text{Length} + \text{Breadth})$
• $\text{Area of Square} = \text{Side} \times \text{Side}$
• $\text{Perimeter of Square} = 4 \times \text{Side}$
• $\text{Area of Triangle} = \frac{1}{2} \times \text{Base} \times \text{Height}$

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

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

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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.