A block of land is represented by the shaded region on the number plane - HSC - SSCE Mathematics Standard - Question 12 - 2021 - Paper 1
Question 12
A block of land is represented by the shaded region on the number plane. All measurements are in kilometres.
Which of the following is the approximation for the are... show full transcript
Worked Solution & Example Answer:A block of land is represented by the shaded region on the number plane - HSC - SSCE Mathematics Standard - Question 12 - 2021 - Paper 1
Step 1
Calculate the area using the trapezoidal rule (first application)
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Answer
To apply the trapezoidal rule, first note the points to be used to approximate the area. We will consider two segments on the x-axis:
From x=0 to x=6:
The function values at these points are: f(0)=1.2 and f(6)=2.
The width of the segment is 6−0=6.
Therefore, the area approximation for this segment is:
A1=21×(f(0)+f(6))×(b−a)=21×(1.2+2)×6=23.2×6=9.6.
Step 2
Calculate the area using the trapezoidal rule (second application)
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Answer
From x=6 to x=12:
The function values are: f(6)=2 and f(12)=1.4.
The width of this segment is 12−6=6.
Therefore, the area approximation for this segment is:
A2=21×(f(6)+f(12))×(b−a)=21×(2+1.4)×6=23.4×6=10.2.
Step 3
Add both areas to calculate the total area
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Answer
The total area is the sum of both calculated areas:
