Area

12 Grade 4 Mathematics questions on Area, with worked marking schemes. 12 questions are available on this topic in full.

1. Question 1

   1 mark

   The area of a path of width 2 m around a 6 m × 4 m garden is ___.

   A. 24 m²

   B. 36 m²

   C. 48 m²

   D. 56 m²

   (1 mark)

   Marking scheme

   D. $56$ m${}^2$ — the path surrounds the garden, so it adds $2$ m at BOTH ends of each side: the outer rectangle is $(6+2+2)\times (4+2+2)=10\times 8=80$ m${}^2$. Taking the garden away leaves the path: $80-24=56$. The option $48$ comes from adding the width only once, giving an $8\times 6$ outer rectangle, and $24$ is the garden itself rather than the path.

2. Question 2

   2 marks

   Otieno's vegetable garden is a rectangle measuring $9$ m long and $5$ m wide. Find the area of the garden.

   (2 marks)

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3. Question 3

   1 mark

   A rectangular exercise book cover measures $6$ cm long and $4$ cm wide. What is its area?

   A. $48{\text{ cm}}^2$

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

   C. $24{\text{ cm}}^2$

   D. $20{\text{ cm}}^2$

   (1 mark)

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4. Question 4

   1 mark

   Which square has the largest area: side 5 cm, 6 cm, 4 cm or 7 cm?

   A. 4 cm side (16 cm²)

   B. 7 cm side (49 cm²)

   C. 5 cm side (25 cm²)

   D. 6 cm side (36 cm²)

   (1 mark)

   Marking scheme

   B. $7$ cm side ($49$ cm${}^2$) — a square's area is side $\times$ side, so the longest side gives the largest area: $7^2=49$ beats $36$, $25$ and $16$. Area grows faster than side length, so the gaps widen.

5. Question 5

   1 mark

   A square has area 100 cm². Find the length of one side.

   A. 50 cm

   B. 25 cm

   C. 10 cm

   D. 5 cm

   (1 mark)

   Marking scheme

   C. $10$ cm — the area of a square is side $\times$ side, so the side is $\sqrt{100}=10$. B and A come from dividing the area by $4$ or $2$ instead of taking the square root.

6. Question 6

   1 mark

   A garden is 12 m long and 9 m wide. What is the area?

   A. 21 m²

   B. 42 m²

   C. 108 m²

   D. 90 m²

   (1 mark)

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7. Question 7

   1 mark

   How many square tiles of side 1 m cover a floor 5 m × 4 m?

   A. 9

   B. 20

   C. 40

   D. 18

   (1 mark)

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8. Question 8

   1 mark

   Find the area of a square with side 7 cm.

   A. 28 cm²

   B. 14 cm²

   C. 42 cm²

   D. 49 cm²

   (1 mark)

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9. Question 9

   1 mark

   A classroom is 10 m × 7 m. What is its area?

   A. 34 m²

   B. 70 m²

   C. 68 m²

   D. 17 m²

   (1 mark)

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10. Question 10

    1 mark

    A rectangle has area 56 cm² and width 7 cm. Find its length.

    A. 6 cm

    B. 8 cm

    C. 7 cm

    D. 9 cm

    (1 mark)

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11. Question 11

    1 mark

    Find the area of a rectangle: length 9 cm, width 5 cm.

    A. 45 cm²

    B. 28 cm²

    C. 40 cm²

    D. 14 cm²

    (1 mark)

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12. Question 12

    1 mark

    A rectangle 12 cm × 4 cm — what is its area?

    A. 16 cm²

    B. 32 cm²

    C. 48 cm²

    D. 44 cm²

    (1 mark)

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