The plan below represents the survey of a farm. Use it to answer questions (a) and (b). (a) Calculate the area of the farmland. (b) If the farmland is plant...
Question 1 Report
The plan below represents the survey of a farm. Use it to answer questions (a) and (b).
(a) Calculate the area of the farmland.
(b) If the farmland is planted with banana at a spacing of 4 m x 4 m, what will be the population of banana plants on the farm?
(c) Study the diagrams labelled I and II below and answer the questions that follow.
(i) Name the tools labelled I and II.
(ii) State two uses of each of the tools labelled I and II.
(iii) State one general way of maintaining the tools labelled I and II.
Answer Details
Reading the plan. The farmland is a trapezium with two parallel sides, the top boundary of \(70\text{ m}\) and the bottom boundary of \(90\text{ m}\), and a perpendicular distance between them (the left boundary) of \(40\text{ m}\).
(a) Area of the farmland
The area of a trapezium is half the sum of the parallel sides multiplied by the perpendicular distance between them:
\[ A = \tfrac{1}{2}(a+b)\times h \]\[ A = \tfrac{1}{2}(70 + 90)\times 40 = \tfrac{1}{2}\times 160 \times 40 \]\[ A = 3200\text{ m}^2 \]The area of the farmland is \(3200\text{ m}^2\) (that is, \(0.32\) hectares).
(b) Population of banana plants
Each plant occupies a square of ground equal to the spacing:
\[ \text{Area per plant} = 4\text{ m} \times 4\text{ m} = 16\text{ m}^2 \]\[ \text{Population} = \frac{\text{Total area}}{\text{Area per plant}} = \frac{3200}{16} = 200 \]The farm can carry a population of 200 banana plants.
(c)(i) Names of the tools
- Tool I: Ranging pole
- Tool II: Arrow / pin
(c)(ii) Two uses of each tool
I (Ranging pole)
- Marking survey stations.
- Setting out straight lines.
II (Arrow / pin)
- Marking off the length of chains measured during chaining.
- Marking survey stations and points of intersection.
(c)(iii) One general way of maintaining the tools
Clean and dry the tools after use, oil or grease the metal parts to prevent rust, and store them in a cool, dry place.
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