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Area Calculation - Trapezoidal Rule


In trapezoidal method, each segment of the section is divided into various trapezoids and triangles.
Trapezoidal Area A = 1/2 X a X (b1+b2)

TrapeZoidalRule

Triangle area A = a * b/2
TropezoidalRule
Example 1:
Area Calculation Trapezoidal Rule
Intersection Point
In the above example, intersection point is between 351 and 354
Filling Height=0.1 @ distance 351
Cutting depth=0.2 @ distance 354
Length from 351 to 354 =3
Distance from 351 to intersection point = 3*[0.1/ (0.1+0.2)] =1 i.e., intersection point is at 352
Cutting Area – Sum of Area of Segment 1, 2, and 3

Sl. No.

Easting

Initial

Level

Final

Level

Difference

Calculation

Area (Sq. meters)

1

345

20.70

20

0.70

2

348

20.50

20

0.50

Segment 1: Area of Trapezoid = ½ * (b1 + b2) * a = ½ * (0.70 + 0.50) * 3

1.80

3

351

20.10

20

0.1

Segment 2: Area of Trapezoid = ½ * (b1 + b2) * a = ½ * (0.50 + 0.10) * 3

0.90

4

352

20.00

20

0

Segment 3: Area of Triangle = ½ * b * h = ½ * 0.1 * 1

0.05

Total

2.75


Filling Area – Sum of Area of Segment 4, 5, 6, and 7

Sl. No.

Easting

Initial

Level

Final

Level

Difference

Calculation

Area

(Sq. meters)

1

352

20.00

20

0.00

2

354

19.80

20

0.20

Segment 4: Area of Triangle = ½ * b * h = ½ * 0.2 * 2

0.20

3

357

19.40

20

0.60

Segment 5: Area of Trapezoid = ½ * (b1 + b2) * a = ½ * (0.20 + 0.60) * 3

1.20

4

360

19.10

20

0.90

Segment 6: Area of Trapezoid = ½ * (b1 + b2) * a = ½ * (0.60 + 0.90) * 3

2.25

5

363

19.00

20

1.00

Segment 7: Area of Trapezoid = ½ * (b1 + b2) * a = ½ * (0.90 + 1.00) * 3

2.85

Total

6.50


Section Method  Section - Nett Area Method