Area

16 Grade 6 Mathematics questions on Area, with worked marking schemes. 16 questions are available on this topic in full.

1. Question 1

   1 mark

   A rectangular plot 60 m by 40 m has a circular fountain of radius 7 m in the middle. What is the area of the remaining land? (Use $\pi =\frac{22}{7}$)

   A. 2,400 m²

   B. 2,246 m²

   C. 154 m²

   D. 2,554 m²

   (1 mark)

   Marking scheme

   B. $2,246$ m${}^2$ — find both areas and subtract. The plot is $60\times 40=2,400$ m${}^2$ and the fountain is $\frac{22}{7}\times 7^2=154$ m${}^2$, so $2,400-154=2,246$. A forgets to remove the fountain.

2. Question 2

   1 mark

   A trapezium has parallel sides 10 cm and 14 cm, height 6 cm. Find its area.

   A. 60 cm²

   B. 84 cm²

   C. 144 cm²

   D. 72 cm²

   (1 mark)

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3. Question 3

   1 mark

   The area of a rhombus with diagonals 12 cm and 16 cm is:

   A. 192 cm²

   B. 28 cm²

   C. 48 cm²

   D. 96 cm²

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4. Question 4

   1 mark

   What is the area of a triangle with base 16 cm and height 10 cm?

   A. 60 cm²

   B. 80 cm²

   C. 26 cm²

   D. 160 cm²

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5. Question 5

   1 mark

   A circular garden has radius 7 m. What is its area? (Use $\pi =\frac{22}{7}$)

   A. 308 m²

   B. 44 m²

   C. 22 m²

   D. 154 m²

   (1 mark)

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6. Question 6

   1 mark

   Two squares have sides 6 cm and 8 cm. What is the difference in their areas?

   A. 2 cm²

   B. 28 cm²

   C. 100 cm²

   D. 14 cm²

   (1 mark)

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7. Question 7

   1 mark

   A square has side 25 m. What is its area?

   A. 125 m²

   B. 100 m²

   C. 625 m²

   D. 50 m²

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8. Question 8

   1 mark

   The area of a rectangle is 180 cm². Its length is 15 cm. Find the width.

   A. 18 cm

   B. 10 cm

   C. 12 cm

   D. 15 cm

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9. Question 9

   1 mark

   A floor is 5 m by 4 m. Square tiles of side 20 cm are used. How many tiles are needed?

   A. 250

   B. 1,000

   C. 100

   D. 500

   (1 mark)

   Marking scheme

   D. $500$ — both measurements must be in the same unit. The floor is $500\times 400=200,000$ cm${}^2$ and each tile is $20\times 20=400$ cm${}^2$, so $200,000÷400=500$. C and A come from dividing lengths rather than areas.

10. Question 10

    1 mark

    A rectangle has length 12 cm and width 8 cm. What is its area?

    A. 80 cm²

    B. 96 cm²

    C. 40 cm²

    D. 20 cm²

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11. Question 11

    1 mark

    A rectangle has length 12 cm and width 8 cm. What is its area?

    A. 80 cm²

    B. 96 cm²

    C. 40 cm²

    D. 20 cm²

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12. Question 12

    1 mark

    A rectangle has length 12 cm and width 8 cm. What is its area?

    A. 40 cm²

    B. 20 cm²

    C. 96 cm²

    D. 80 cm²

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13. Question 13

    1 mark

    A farm is 400 m by 250 m. What is its area in hectares? (1 ha = 10,000 m²)

    A. 100 ha

    B. 10 ha

    C. 1 ha

    D. 1,000 ha

    (1 mark)

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14. Question 14

    1 mark

    The area of a circle is 616 cm². What is its radius? (Use $\pi =\frac{22}{7}$)

    A. 28 cm

    B. 21 cm

    C. 7 cm

    D. 14 cm

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15. Question 15

    1 mark

    Find the area of a parallelogram with base 14 cm and height 9 cm.

    A. 126 cm²

    B. 23 cm²

    C. 46 cm²

    D. 63 cm²

    (1 mark)

    Marking scheme

    A. $126$ cm${}^2$ — a parallelogram has the same area as a rectangle on the same base: base $\times$ perpendicular height $=14\times 9$. D halves it, which is the triangle rule, not this one.

16. Question 16

    1 mark

    How many square centimetres make 1 m²?

    A. 100

    B. 100,000

    C. 10,000

    D. 1,000

    (1 mark)

    Marking scheme

    C. $10,000$ — a square metre is $100$ cm by $100$ cm, so it holds $100\times 100=10,000$ square centimetres. A is the conversion for length, not area — area conversions square the factor.

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