1. Area calculation

2. Area is divided into triangles, rectangles, squares or trapeziums
Area of the one figure (e.g. triangles, rectangles, squares or trapeziums) is calculated and multiplied by total number of figures.
Area along the boundaries is calculated as
Total area of the filed=area of geometrical figure boundary areas

3. Problem-1

4. Problem 1-Result

7. Computation of area from plotted plan
Boundary area can be calculated as one of the following rule:
The mid-ordinate rule
The average ordinate rule
The trapezoidal rule
Simpson’s rule

8. Mid-ordinate rule l

9. Average ordinate rule

10. Trapezoidal rule

11. Simpson’s rule

12. Problems
The following perpendicular offsets were taken from chain line to an irregular boundary:
Chainage m
offset
Calculate the area between the chain line, the boundary and the end offsets.
The following perpendicular offsets were taken from a chain line to a hedge:
Calculate the area by mid ordinate and Simpson’s rule.
chainage 15 30 45 60 70 80
100
120
140
offsets
7.6
8.5
10.7
12.8
10.6
9.5
8.3
7.9
6.4
4.4

13. Area by double meridian distances
Meridian distance of any point in a traverse is the distance of that point to the reference meridian, measured at right angle to the meridian.
The meridian distance of a survey line is defined as the meridian distance of its mid point.
The meridian distance sometimes called as the longitude.

14. d4/2
d4/2
d3/2
d3/2 D d m4 m3 4 3
Mid points
Meridian distance of points (d1, d2, d3, d4) A c C 1 B 2 b
d1/2
d1/2
d2/2
d2/2 m1 m2

15. Meridian distances of survey line:
m1=d1/2
m2= m1+d1/2+d2/2
m3=m2+d2/2-d3/2
m4=m3-d3/2-d4/2
Area by latitude and meridian distance
Area of ABCD=area of trapezium CcdD + area of trapezium CcbB – area of triangle AbB – area of triangle AdD
= m3*L3+ m2*L2-1/2*2*m4*L4-1/2*2*m1*L1
=m3*L3+m2*L2-m4*L4-m1*L1

16. Double meridian distance:
M1= meridian distance of point A + meridian distance of point B
M1=0+d1
M2=meridian distance of point B + meridian distance of point C
=d1+(d1+d2)
=M1+(d1+d2)
M3=(d1+d2)+(d1+d2-d3)

17. Area of the traverse ABCD = M3*L3+M2*L2-M1*L1-M4*L4
Area by Co-Ordinates

18. The following table gives the corrected latitudes and departures (in m) of the sides of a closed traverse ABCD. Compute the area by (a) M.D. method (b) co-ordinate method
Side
Latitude
Departure N S E W AB
108 4 BC 15
249 CD
123 DA
257

19. Volume calculation
From cross sections
From spot levels
From contours

20. Measurement of volume
3 methods generally adopted for measuring the volume are
(i) from cross sections
(ii) from spot levels
(iii) from contours

22. Methods of volume calculation
Prismoidal method D2 A2 C2 B2 D2 D1 A2 A1 C1 C2 B1 B2 D1 A1 B1 C1

23. Also called Simpson’s rule for volume.
Necessary to have odd number of cross sections.
What if there are even number of C/S?
Trapezoidal method:
Assumption mid area is mean of end areas.
Volume =d{(A1+An)/2+A2+A3+…+An-1}

24. A railway embankment is 10 m wide with side slopes 1. 5:1
A railway embankment is 10 m wide with side slopes 1.5:1. assuming the ground to be level in a direction transverse to the centre line, calculate the volume contained in a length of 120 m, the centre heights at 20 m intervals being in metres 2.2, 3.7, 3.8, 4.0, 3.8, 2.8, 2.5.
A railway embankment 400 m long is 12 m wide at the formation level and has the side slope 2:1. The ground levels across the centre line are as under:
The formation level at zero chainage is and the embankment has a rising gradient of 1:100. The ground is level across the centre line. Calculate the volume of earthwork.
Distance
100
200
300
400
R.L.
204.8
206.2
207.5
207.2
208.3