Figure 2 shows a plan view of a garden. The plan of the garden ABCDEA consists of a triangle ABE joined to a sector BCDE of a circle with radius 12 m and centre B. The points A, B and C lie on a straight line with AB = 23 m and BC = 12 m. Given that the size of angle ABE is exactly 0.64 radians, find (a) the area of the garden, giving your answer in m², to 1 decimal place. (b) the perimeter of the garden, giving your answer in metres, to 1 decimal place.

A-Level Edexcel Maths Pure Solving Equations: Figure 2 shows a plan view of a

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

Question 7

Figure 2 shows a plan view of a garden. The plan of the garden ABCDEA consists of a triangle ABE joined to a sector BCDE of a circle with radius 12 m and centre B. T... show full transcript

Worked Solution & Example Answer:Figure 2 shows a plan view of a garden - Edexcel - A-Level Maths Pure - Question 7 - 2013 - Paper 4

Step 1

(a) the area of the garden, giving your answer in m², to 1 decimal place.

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Answer

To find the area of triangle ABE, we can use the formula:

Area = \frac{1}{2} \times AB \times AE \times \sin(\text{angle ABE})

Given:

(AB = 23 , m)
(\text{angle ABE} = 0.64 , radians)
We need to find (AE). Using the sine rule:

\frac{AE}{\sin(\text{angle ABE})} = \frac{AB}{\sin(CDE)}

Calculating the area:

Area = \frac{1}{2} \times 23 \times 12 \times \sin(0.64) \approx 26.3 \, m^{2}

Final answer:

The area of the garden is approximately 26.3 m².

Step 2

(b) the perimeter of the garden, giving your answer in metres, to 1 decimal place.

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Answer

The perimeter consists of the sum of the lengths of all the sides:

Side AB: 23 m
Side BC: 12 m
The arc length of the sector BCDE: We need to calculate this using the formula:

ext{Arc Length} = r \times \theta

where (r = 12 , m) and (\theta = 0.64). Thus, the arc length is:

\text{Arc Length} = 12 \times 0.64 \approx 7.68 \, m

Now, adding all components for the perimeter:

P = AB + BC + \text{Arc Length} = 23 + 12 + 7.68 = 42.68 \, m

Final answer:

The perimeter of the garden is approximately 42.7 m.

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

Worked Solution & Example Answer:Figure 2 shows a plan view of a garden - Edexcel - A-Level Maths Pure - Question 7 - 2013 - Paper 4

(a) the area of the garden, giving your answer in m², to 1 decimal place.

(b) the perimeter of the garden, giving your answer in metres, to 1 decimal place.

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