The diagram shows a plan of Jason’s garden - Edexcel - GCSE Maths - Question 4 - 2022 - Paper 2

The area of rectangle DEFO can also be calculated:

$\text{Area} = \text{length} \times \text{width}$

The length DE is 9 m and the width DO (or EF) is 7 m:

$\text{Area of DEFO} = 9 \text{ m} \times 7 \text{ m} = 63 \text{ m}^2$

The area of triangle CDO can be calculated using the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Using CD as the base (7 m) and CO as the height (7 m):

$\text{Area of triangle CDO} = \frac{1}{2} \times 7 \text{ m} \times 7 \text{ m} = 24.5 \text{ m}^2$

The area of the sector AFO with radius 4 m and angle 90° can be calculated as:

$\text{Area} = \frac{\theta}{360} \times \pi r^2$

Here, (\theta = 90°) and (r = 4) m:

$\text{Area of sector AFO} = \frac{90}{360} \times \pi \times (4)^2 = \frac{1}{4} \times \pi \times 16 = 4\pi \approx 12.57 \text{ m}^2$

Now, we sum the areas calculated:

$\text{Total Area} = \text{Area of ABCO} + \text{Area of DEFO} + \text{Area of triangle CDO} + \text{Area of sector AFO}$

Substituting the values:

$\text{Total Area} = 77 + 63 + 24.5 + 12.57 = 177.07 \text{ m}^2$

Since each bag covers 14 m², we find the number of bags needed:

$\text{Number of bags} = \frac{\text{Total Area}}{\text{Area per bag}} = \frac{177.07}{14} \approx 12.64$

Rounding up, Jason needs 13 bags.

The total cost for the grass seed is calculated by:

$\text{Total Cost} = \text{Number of bags} \times \text{Cost per bag}$

Thus,

$\text{Total Cost} = 13 \times 10.95 = 142.35\text{ £}$