Figure 2 shows a plan view of a garden - Edexcel - A-Level Maths Pure - Question 7 - 2013 - Paper 4

To find the area of the garden, we need to calculate the area of triangle ABE and the area of sector BCDE.

1. Area of Triangle ABE: The formula for the area of a triangle is:

   $ext{Area}_{ABE} = \frac{1}{2} \times AB \times AE \times \sin(\theta)$ where ( \theta = 0.64) radians and ( AB = 23) m.

   Since we first need to calculate AE using the Cosine Rule:

   $AE^2 = AB^2 + BE^2 - 2(AB)(BE)\cos(\theta)$ We find that AE is approximately 19.106 m.

   Therefore, the area is:

   $\text{Area}_{ABE} = \frac{1}{2} \times 23 \times 19.106 \times \sin(0.64) \approx 82.4 m^2.$

2. Area of Sector BCDE: The formula for the area of a sector is:

   $ext{Area}_{sector} = \frac{1}{2} r^2 \theta$ where ( r = 12 ) m and ( \theta = 0.64 ) radians.

   Therefore, the area of the sector is:

   $\text{Area}_{sector} = \frac{1}{2} \times 12^2 \times 0.64 \approx 46.08 m^2.$

3. Total Area of the Garden:

   $\text{Total Area} = \text{Area}_{ABE} + \text{Area}_{sector} \approx 82.4 + 46.08 = 128.48 m^2.$

Thus rounding to 1 decimal place, the area is:

Answer: The area of the garden is approximately 128.5 m².