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Find the area of the traverse using Simpson’s rule if d= 12 m and the values of ordinates are 2.25m, 1.46m, 3.23m, 4.46m.
- a)116.88 sq. m
- b)161.88 sq. m
- c)611.88 sq. m
- d)169.54 sq. m
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Find the area of the traverse using Simpson’s rule if d= 12 m an...
To find the area of a traverse using Simpson's rule, we need the coordinates of the points in the traverse. Let's assume that we have the following coordinates:
Point A: (x1, y1)
Point B: (x2, y2)
Point C: (x3, y3)
Point D: (x4, y4)
Point E: (x5, y5)
Simpson's rule states that the area under a curve can be approximated by dividing the curve into equally spaced intervals and using quadratic polynomials to approximate the curve within each interval.
To apply Simpson's rule to our traverse, we will divide the traverse into subintervals AB, BC, CD, and DE. We will then use Simpson's rule to find the area under each subinterval curve, and sum up the areas to find the total area of the traverse.
The formula for the area under a curve using Simpson's rule is:
Area = (h/3) * (y1 + 4y2 + 2y3 + 4y4 + y5)
Where h is the distance between each point (h = (x2 - x1), which is assumed to be the same for all subintervals), and y1, y2, y3, y4, y5 are the corresponding y-coordinates of each point.
Let's calculate the area for each subinterval and sum them up to find the total area of the traverse:
Area_AB = (h/3) * (y1 + 4y2 + y3)
Area_BC = (h/3) * (y3 + 4y4 + y5)
Total Area = Area_AB + Area_BC
Note that if you have more points in the traverse, you will need to divide the traverse into more subintervals and use Simpson's rule for each subinterval to find the total area.
Point A: (x1, y1)
Point B: (x2, y2)
Point C: (x3, y3)
Point D: (x4, y4)
Point E: (x5, y5)
Simpson's rule states that the area under a curve can be approximated by dividing the curve into equally spaced intervals and using quadratic polynomials to approximate the curve within each interval.
To apply Simpson's rule to our traverse, we will divide the traverse into subintervals AB, BC, CD, and DE. We will then use Simpson's rule to find the area under each subinterval curve, and sum up the areas to find the total area of the traverse.
The formula for the area under a curve using Simpson's rule is:
Area = (h/3) * (y1 + 4y2 + 2y3 + 4y4 + y5)
Where h is the distance between each point (h = (x2 - x1), which is assumed to be the same for all subintervals), and y1, y2, y3, y4, y5 are the corresponding y-coordinates of each point.
Let's calculate the area for each subinterval and sum them up to find the total area of the traverse:
Area_AB = (h/3) * (y1 + 4y2 + y3)
Area_BC = (h/3) * (y3 + 4y4 + y5)
Total Area = Area_AB + Area_BC
Note that if you have more points in the traverse, you will need to divide the traverse into more subintervals and use Simpson's rule for each subinterval to find the total area.
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Find the area of the traverse using Simpson’s rule if d= 12 m an...
The formula for Simpson’s rule can be given as Δ = (d/3)*((O0+O4) + 4*(O1+O3) + 2*(O2+O4)). On substitution, we get
Δ = (12/3)* ((2.25+4.46) + 4*(2.25+3.23) + 2*(1.46+4.46))
Δ = 161.88 sq. m.
Δ = (12/3)* ((2.25+4.46) + 4*(2.25+3.23) + 2*(1.46+4.46))
Δ = 161.88 sq. m.
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Find the area of the traverse using Simpson’s rule if d= 12 m and the values of ordinates are 2.25m, 1.46m, 3.23m, 4.46m.a)116.88 sq. mb)161.88 sq. mc)611.88 sq. md)169.54 sq. mCorrect answer is option 'B'. Can you explain this answer?
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Find the area of the traverse using Simpson’s rule if d= 12 m and the values of ordinates are 2.25m, 1.46m, 3.23m, 4.46m.a)116.88 sq. mb)161.88 sq. mc)611.88 sq. md)169.54 sq. mCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Find the area of the traverse using Simpson’s rule if d= 12 m and the values of ordinates are 2.25m, 1.46m, 3.23m, 4.46m.a)116.88 sq. mb)161.88 sq. mc)611.88 sq. md)169.54 sq. mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the area of the traverse using Simpson’s rule if d= 12 m and the values of ordinates are 2.25m, 1.46m, 3.23m, 4.46m.a)116.88 sq. mb)161.88 sq. mc)611.88 sq. md)169.54 sq. mCorrect answer is option 'B'. Can you explain this answer?.
Find the area of the traverse using Simpson’s rule if d= 12 m and the values of ordinates are 2.25m, 1.46m, 3.23m, 4.46m.a)116.88 sq. mb)161.88 sq. mc)611.88 sq. md)169.54 sq. mCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Find the area of the traverse using Simpson’s rule if d= 12 m and the values of ordinates are 2.25m, 1.46m, 3.23m, 4.46m.a)116.88 sq. mb)161.88 sq. mc)611.88 sq. md)169.54 sq. mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the area of the traverse using Simpson’s rule if d= 12 m and the values of ordinates are 2.25m, 1.46m, 3.23m, 4.46m.a)116.88 sq. mb)161.88 sq. mc)611.88 sq. md)169.54 sq. mCorrect answer is option 'B'. Can you explain this answer?.
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Find the area of the traverse using Simpson’s rule if d= 12 m and the values of ordinates are 2.25m, 1.46m, 3.23m, 4.46m.a)116.88 sq. mb)161.88 sq. mc)611.88 sq. md)169.54 sq. mCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Find the area of the traverse using Simpson’s rule if d= 12 m and the values of ordinates are 2.25m, 1.46m, 3.23m, 4.46m.a)116.88 sq. mb)161.88 sq. mc)611.88 sq. md)169.54 sq. mCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Find the area of the traverse using Simpson’s rule if d= 12 m and the values of ordinates are 2.25m, 1.46m, 3.23m, 4.46m.a)116.88 sq. mb)161.88 sq. mc)611.88 sq. md)169.54 sq. mCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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