Area

14 Grade 8 Mathematics questions on Area, with worked marking schemes. 14 questions are available on this topic in full.

1. Question 1

   4 marks

   A closed cylinder has radius 7 cm and height 20 cm. (Take pi = 22/7)

   (a) Find the area of one circular base. (2 marks)

   (b) Find the curved surface area. (2 marks)

   Marking scheme

   (a) A circular base has area $\pi r^2$. With $r=7$ cm and $\pi =\frac{22}{7}$: $\frac{22}{7}\times 7^2$. (1)

   $7^2=49$, and $\frac{22}{7}\times 49=22\times 7=154$ cm${}^2$. (1)

   (b) The curved surface unrolls into a rectangle whose width is the circumference and whose height is the height of the cylinder, so its area is $2\pi rh$. (1)

   Substitute: $2\times \frac{22}{7}\times 7\times 20=2\times 22\times 20=880$ cm${}^2$. (1)

   Final answer: the base area is $154$ cm${}^2$ and the curved surface area is $880$ cm${}^2$.

2. Question 2

   3 marks

   A circular garden has radius 14 m. Taking pi = 22/7, find its area and the cost of planting grass at Ksh 50 per square metre.

   (3 marks)

   Marking scheme

   The area of a circle is $\pi r^2$. With $r=14$ m and $\pi =\frac{22}{7}$: $\frac{22}{7}\times 14^2$. (1)

   $14^2=196$, and $\frac{22}{7}\times 196=22\times 28=616$ m${}^2$. (1)

   The grass costs Ksh $50$ for each square metre, so multiply: $616\times 50=30,800$. (1)

   Final answer: the area is $616$ m${}^2$ and the cost is Ksh $30,800$.

3. Question 3

   3 marks

   Find the total surface area of a closed rectangular box measuring 10 cm by 6 cm by 4 cm.

   (3 marks)

   Marking scheme

   A closed box has three pairs of identical faces, so the surface area is $2(lw+lh+wh)$. (1)

   Substitute $l=10$, $w=6$, $h=4$: $lw=60$, $lh=40$, $wh=24$. (1)

   Add and double: $2(60+40+24)=2\times 124=248$. (1)

   Final answer: $248$ cm${}^2$.

4. Question 4

   1 mark

   Find the area of a trapezium with parallel sides 6 cm and 10 cm and height 4 cm.

   A. 32 cm²

   B. 64 cm²

   C. 40 cm²

   D. 16 cm²

   (1 mark)

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5. Question 5

   1 mark

   Find the area of a circle of diameter 28 cm. (Take pi = 22/7)

   A. 2464 cm²

   B. 616 cm²

   C. 154 cm²

   D. 88 cm²

   (1 mark)

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6. Question 6

   3 marks

   A rectangular plot measures 40 m by 25 m. Find its perimeter and the cost of fencing it at Ksh 150 per metre.

   (3 marks)

   Marking scheme

   Fencing goes around the plot, so this is the perimeter: $2(\text{length}+\text{width})$. (1)

   Substitute $40$ m and $25$ m: $2(40+25)=2\times 65=130$ m. (1)

   The fence costs Ksh $150$ for each metre, so multiply: $130\times 150=19,500$. (1)

   Final answer: the perimeter is $130$ m and the cost is Ksh $19,500$.

7. Question 7

   1 mark

   Find the area of a sector of angle 90 degrees in a circle of radius 14 cm. (Take pi = 22/7)

   A. 154 cm²

   B. 616 cm²

   C. 38.5 cm²

   D. 77 cm²

   (1 mark)

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8. Question 8

   1 mark

   Find the area of a circle of radius 21 cm. (Take pi = 22/7)

   A. 132 cm²

   B. 66 cm²

   C. 1386 cm²

   D. 693 cm²

   (1 mark)

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9. Question 9

   1 mark

   Find the area of a triangle with base 12 cm and height 5 cm.

   A. 30 cm²

   B. 60 cm²

   C. 17 cm²

   D. 120 cm²

   (1 mark)

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10. Question 10

    1 mark

    Find the area of a circle of radius 7 cm. (Take pi = 22/7)

    A. 44 cm²

    B. 49 cm²

    C. 22 cm²

    D. 154 cm²

    (1 mark)

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11. Question 11

    1 mark

    Find the total surface area of a cuboid measuring 4 cm by 3 cm by 2 cm.

    A. 24 cm²

    B. 26 cm²

    C. 104 cm²

    D. 52 cm²

    (1 mark)

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12. Question 12

    1 mark

    Find the total surface area of a cube of side 5 cm.

    A. 125 cm²

    B. 25 cm²

    C. 150 cm²

    D. 100 cm²

    (1 mark)

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13. Question 13

    1 mark

    Find the area of a rectangle measuring 12 cm by 8 cm.

    A. 40 cm²

    B. 96 cm²

    C. 20 cm²

    D. 192 cm²

    (1 mark)

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14. Question 14

    1 mark

    Find the total surface area of a closed cylinder of radius 7 cm and height 10 cm. (Take pi = 22/7)

    A. 440 cm²

    B. 748 cm²

    C. 594 cm²

    D. 880 cm²

    (1 mark)

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