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 ...

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.