Area

16 Grade 7 Mathematics questions on Area, with worked marking schemes. 16 questions are available on this topic in full.

1. Question 1

   2 marks

   Calculate the area of a triangle with base 10 cm and height 6 cm.

   (2 marks)

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2. Question 2

   3 marks

   Find the area of a semicircle of diameter 28 cm. (Use $\pi =\frac{22}{7}$)

   (3 marks)

   Marking scheme

   The radius is half the diameter: $r=\frac{28}{2}=14$ cm. (1)

   A full circle has area $\pi r^2=\frac{22}{7}\times 14^2=\frac{22}{7}\times 196=616$ cm${}^2$. (1)

   A semicircle is half of that: $\frac{1}{2}\times 616=308$. (1)

   Final answer: $308$ cm${}^2$.

3. Question 3

   2 marks

   Calculate the area of a triangle with base 10 cm and height 6 cm.

   (2 marks)

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4. Question 4

   1 mark

   A circle has radius 7 cm. What is the area? ($\pi =\frac{22}{7}$)

   A. 44 cm²

   B. 308 cm²

   C. 22 cm²

   D. 154 cm²

   (1 mark)

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5. Question 5

   1 mark

   A rhombus has diagonals 10 cm and 24 cm. Area = ?

   A. 240 cm²

   B. 60 cm²

   C. 34 cm²

   D. 120 cm²

   (1 mark)

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6. Question 6

   3 marks

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

   (3 marks)

   Marking scheme

   The area of a circle is $\pi r^2$, so $\frac{22}{7}{r}^2=616$. (1)

   Multiply both sides by $\frac{7}{22}$ to leave $r^2$ alone: $r^2=616\times \frac{7}{22}=196$. (1)

   Take the square root: $r=\sqrt{196}=14$. (1)

   Final answer: $14$ cm.

7. Question 7

   4 marks

   A circular flower bed has radius 3.5 m surrounded by a 1.5 m path. Find the area of the path. (Use $\pi =\frac{22}{7}$)

   (4 marks)

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8. Question 8

   1 mark

   A rectangular plot 80 m by 60 m has a 2 m wide path inside. What is the path area?

   A. 480 m²

   B. 544 m²

   C. 4,256 m²

   D. 560 m²

   (1 mark)

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9. Question 9

   1 mark

   The area of a sector with radius 14 cm and angle 90° is: ($\pi =\frac{22}{7}$)

   A. 308 cm²

   B. 616 cm²

   C. 154 cm²

   D. 44 cm²

   (1 mark)

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10. Question 10

    1 mark

    Find the area of a triangle with sides 5 cm, 12 cm and 13 cm.

    A. 65 cm²

    B. 30 cm²

    C. 78 cm²

    D. 60 cm²

    (1 mark)

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11. Question 11

    5 marks

    A rectangular plot of land measures 80 m by 60 m. A path of width 2 m runs around the inside of the plot.

    (a) Calculate the area of the path. (3 marks)

    (b) If the path is to be paved at a cost of Ksh 450 per square metre, find the total cost. (2 marks)

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12. Question 12

    1 mark

    A trapezium has parallel sides 8 cm and 12 cm, height 5 cm. Area = ?

    A. 100 cm²

    B. 60 cm²

    C. 50 cm²

    D. 48 cm²

    (1 mark)

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13. Question 13

    3 marks

    Solve the inequality and represent the solution on a number line:

    $$3x-5\le 7$$

    (3 marks)

    Marking scheme

    Add $5$ to both sides to leave the $x$ term on its own: $3x\le 12$. (1)

    Divide both sides by $3$. Dividing by a positive number keeps the inequality the same way round: $x\le 4$. (1)

    On the number line, draw a closed circle at $4$ because $4$ is included, and shade everything to the left of it. (1)

    Final answer: $x\le 4$.

14. Question 14

    5 marks

    A rectangular plot of land measures 80 m by 60 m. A path of width 2 m runs around the inside of the plot.

    (a) Calculate the area of the path. (3 marks)

    (b) If the path is to be paved at a cost of Ksh 450 per square metre, find the total cost. (2 marks)

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15. Question 15

    3 marks

    Solve the inequality and represent the solution on a number line:

    $$3x-5\le 7$$

    (3 marks)

    Marking scheme

    Add $5$ to both sides to leave the $x$ term on its own: $3x\le 12$. (1)

    Divide both sides by $3$. Dividing by a positive number keeps the inequality the same way round: $x\le 4$. (1)

    On the number line, draw a closed circle at $4$ because $4$ is included, and shade everything to the left of it. (1)

    Final answer: $x\le 4$.

16. Question 16

    5 marks

    A rectangular plot 80 m × 60 m has a path 2 m wide inside.

    (a) Find the area of the path. (3 marks)

    (b) If paving costs Ksh 450/m², find the total cost. (2 marks)

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