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 12m and centre B. The points A, B and C lie on a straight line with AB = 23m and BC = 12m. 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 Integration: Figure 2 shows a plan view of a

Figure 2 shows a plan view of a garden - Edexcel - A-Level Maths Pure - Question 6 - 2013 - Paper 4

Question 6

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 12m and centre B. Th... show full transcript

Worked Solution & Example Answer:Figure 2 shows a plan view of a garden - Edexcel - A-Level Maths Pure - Question 6 - 2013 - Paper 4

Step 1

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

96%

114 rated

Answer

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

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

$ext{Area} = \frac{1}{2} \times a \times b \times \sin(C)$

where ( a = 23,m ), ( b = 12,m ), and ( C = 0.64 \text{ radians} ).

Substituting the values:

$ext{Area} = \frac{1}{2} \times 23 \times 12 \times \sin(0.64)$

Calculating this gives: $\text{Area} \approx 82.4\,m^2$ (to 1 decimal place).
Area of Sector BCDE: The formula for the area of a sector is:

$ext{Area} = \frac{1}{2} r^2 \theta$

where ( r = 12,m ) and ( \theta = 0.64, ext{radians} ).

Substituting the values:

$\text{Area} \approx \frac{1}{2} \times 12^2 \times 0.64 \approx 38.4\,m^2$ .
Total Area of the Garden:

$\text{Total Area} \approx 82.4 + 38.4 \approx 120.8\,m^2$

Thus, the area of the garden is approximately 120.8 m².

Step 2

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

99%

104 rated

Answer

The perimeter of the garden consists of three parts: the length AB, the radius BC, and the arc length of sector BCDE.

Length AB: Given as ( AB = 23,m ).
Length BC: Given as ( BC = 12,m ).
Arc Length of Sector BCDE: The arc length can be calculated using the formula:

$L = r \theta$ where ( r = 12,m ) and ( \theta = 0.64 \text{ radians} ).

Substituting the values gives:

$L = 12 \times 0.64 \approx 7.68\,m$ .
Total Perimeter of the Garden:

$ext{Perimeter} = AB + BC + L = 23 + 12 + 7.68 \approx 42.68\,m$

Thus, the perimeter of the garden is approximately 42.7 m (to 1 decimal place).

Figure 2 shows a plan view of a garden - Edexcel - A-Level Maths Pure - Question 6 - 2013 - Paper 4

Worked Solution & Example Answer:Figure 2 shows a plan view of a garden - Edexcel - A-Level Maths Pure - Question 6 - 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.

Join the A-Level students using SimpleStudy...