The diagram represents a rectangular garden of length 10m and width 8m - OCR - GCSE Maths - Question 10 - 2017 - Paper 1

The flower bed is a triangle with a base of 2m and a height of 6m. The area of a triangle is calculated using:

$$ext{Area} = \frac{1}{2} \times ext{base} \times ext{height} = \frac{1}{2} \times 2 ext{m} \times 6 ext{m} = 6 ext{m}^2$$

The patio is a trapezium with bases of 5m and 8m, and a height of 3m. The area of a trapezium is calculated using:

$$ext{Area} = \frac{1}{2} \times (b_1 + b_2) \times h = \frac{1}{2} \times (5 ext{m} + 8 ext{m}) \times 3 ext{m} = \frac{1}{2} \times 13 ext{m} \times 3 ext{m} = 19.5 ext{m}^2$$

To find the area of the lawn, we subtract the areas of the flower bed and the patio from the area of the entire garden:

$$ext{Area of lawn} = ext{Area of garden} - ( ext{Area of flower bed} + ext{Area of patio})$$

Calculating this gives:

$$ext{Area of lawn} = 80 ext{m}^2 - (6 ext{m}^2 + 19.5 ext{m}^2) = 80 ext{m}^2 - 25.5 ext{m}^2 = 54.5 ext{m}^2$$