Here's the question:
Determine the enclosed area by calculating the area of triangle ABC and adding on the area contained within the irregular boundary and straight line AC. This latter area should be calculated using Simpson's rule and the trapezoidal rule, and a comparison made of the resulting areas.
Here's my calculation (Is my calculation right ?):
Triangle ABC, by Heron's formula:
s = (470 + 550 + 770)/2 = 895
Area of Triangle ABC = [895 x (895-470) x (895-550) x (895-770)]^1/2 = 128076.8202m2
Irregular Area, by trapezoidal rule:
Area = 110 x [(0+12.5)/2 + (12.5+15)/2 + (15+10.7)/2 + (10.7+19.6)/2 + (19.6+8.7)/2 + (8.7+5)/2 + (5+0)/2] = 7865m2
Irregular Area, by Simpson's rule:
Here's my question, as I know the Simpson's rule is base on the interval must be divided into an even number of segments of equal width then producing an odd number of ordinates, now what to do if there are an even number of ordinates as above ???
Simpson's rule: Area = interval / 3 [O1 + On + 2(O3+O5+O7+...) + 4(O2+O4+O6+...)], that n must be even.
What is the purpose of the calculation of Triangle ABC area ?
Please help and thx a lot !
| Line | AB | BC | CA |
| Length(m) | 470 | 550 | 770 |
| Chainage from A(m) | 0 | 110 | 220 | 330 | 440 | 550 | 660 | 770 |
| Offset(m) | 0 | 12.5 | 15.0 | 10.7 | 19.6 | 8.7 | 5.0 | 0 |
Determine the enclosed area by calculating the area of triangle ABC and adding on the area contained within the irregular boundary and straight line AC. This latter area should be calculated using Simpson's rule and the trapezoidal rule, and a comparison made of the resulting areas.
Here's my calculation (Is my calculation right ?):
Triangle ABC, by Heron's formula:
s = (470 + 550 + 770)/2 = 895
Area of Triangle ABC = [895 x (895-470) x (895-550) x (895-770)]^1/2 = 128076.8202m2
Irregular Area, by trapezoidal rule:
Area = 110 x [(0+12.5)/2 + (12.5+15)/2 + (15+10.7)/2 + (10.7+19.6)/2 + (19.6+8.7)/2 + (8.7+5)/2 + (5+0)/2] = 7865m2
Irregular Area, by Simpson's rule:
Here's my question, as I know the Simpson's rule is base on the interval must be divided into an even number of segments of equal width then producing an odd number of ordinates, now what to do if there are an even number of ordinates as above ???
Simpson's rule: Area = interval / 3 [O1 + On + 2(O3+O5+O7+...) + 4(O2+O4+O6+...)], that n must be even.
What is the purpose of the calculation of Triangle ABC area ?
Please help and thx a lot !
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