A farmer has a field that is in the shape of a trapezium - OCR - GCSE Maths - Question 12 - 2017 - Paper 1

To find the area of the trapezium, we can use the formula:

$ext{Area} = \frac{(a + b) \times h}{2}$

Where:

• $a = 180 \text{m}$ (one base)
• $b = 220 \text{m}$ (the other base)
• $h = 150 \text{m}$ (height)

Calculating the area:

$ext{Area} = \frac{(180 + 220) \times 150}{2} = \frac{400 \times 150}{2} = 30000 \text{m}^2$

Next, we convert the area into hectares:

$1 \text{ hectare} = 10000 \text{m}^2 \Rightarrow \text{Area in hectares} = \frac{30000}{10000} = 3 \text{ hectares}$

Now, we calculate the total kilograms of wheat produced:

$\text{Kilograms of wheat} = \text{Area in hectares} \times 6400 = 3 \times 6400 = 19200 \text{ kg}$