The plan below represents the survey of a school farm. Use it to answer Questions (a) and (b). (a) Calculate the area of the land in hectares [4 marks] 70m ...
Question 1 Report
The plan below represents the survey of a school farm.
Use it to answer Questions (a) and (b).
(a) Calculate the area of the land in hectares [4 marks] 70m
(b) If the school plans to cultivate plantain at a spacing of 4m x 4m on 80% of the land and pineapple at a spacing of 2m x 2.5m on 20% of the land, calculate the number of plantain and pineapple planting materials that would be required for the farm. [12 marks]
Answer Details
Reading the plan. The farm is a trapezium with the two parallel boundaries measuring 70 m (top, BC) and 90 m (bottom, AD), and the perpendicular distance between them AB = 45 m.
(a) Area of the land in hectares
\[ \text{Area} = \tfrac{1}{2}(BC + AD)\times AB = \tfrac{1}{2}(70 + 90)\times 45 \] \[ = \tfrac{1}{2}\times 160 \times 45 = 80 \times 45 = 3600\ \text{m}^2 \]Converting to hectares, using \(1\ \text{hectare} = 10\,000\ \text{m}^2\):
\[ \text{Area} = \frac{3600}{10\,000} = 0.36\ \text{hectares} \](b) Number of planting materials required
Step 1: Share the land between the crops.
\[ \text{Plantain area} = \frac{80}{100}\times 3600 = 2880\ \text{m}^2 \] \[ \text{Pineapple area} = \frac{20}{100}\times 3600 = 720\ \text{m}^2 \]Step 2: Ground area occupied by one plant.
\[ \text{Plantain: } 4\ \text{m} \times 4\ \text{m} = 16\ \text{m}^2 \] \[ \text{Pineapple: } 2\ \text{m} \times 2.5\ \text{m} = 5\ \text{m}^2 \]Step 3: Number of plants = crop area ÷ area per plant.
\[ \text{Plantain} = \frac{2880}{16} = 180\ \text{stands} \] \[ \text{Pineapple} = \frac{720}{5} = 144\ \text{stands} \]| Crop | Area (m2) | Spacing | m2 per plant | Plants |
|---|---|---|---|---|
| Plantain | 2880 | 4 m x 4 m | 16 | 180 |
| Pineapple | 720 | 2 m x 2.5 m | 5 | 144 |
The farm requires 180 plantain suckers and 144 pineapple suckers.
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