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...

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.