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1. Soil and Water Conservation Engineering
SWE 112 (1+1)
Practical 2
Computation of Area by Chain and Cross
Staff Survey

2. Computation of Area by Chain and Cross Staff Survey
Aim
To locate the boundaries of the given field and also to
determine the area (by chain and cross staff survey)
Instruments required
Chain, cross staff, arrows, ranging rods

3. Computation of Area by Chain and Cross Staff Survey
Procedure
In order to calculate the area of any piece of land which
is irregular in shape it is necessary to divide the area into
number of right angled triangles and trapezoidal in
shape.
Corners along the boundary of the field should be first
identified and named as A,B,C,D,E,F and G. any two
stations located in opposite sides should be selected in
such a way that distance between them is the longest of
other stations and almost equal number of corners
(stations) are located on both sides.

4. Computation of Area by Chain and Cross Staff Survey
Procedure
Chaining should be started along the base line and off set
distance of the corners on both sides are to be measured
simultaneously.
All the details should be entered in the field observation
book.
Care should be taken that no offset is over looked before
the chain is moved forward.

5. Computation of Area by Chain and Cross Staff Survey
Procedure
To check the accuracy of the field, work distance
between any two corners should be measured directly
and compared.
After the field work is over the survey may be plotted to
a suitable scale.
The area enclosed by the boundary lines is divided into a
number of triangles and trapezoids.

6. Computation of Area by Chain and Cross Staff Survey
Procedure
The area of each segment may be plotted to a suitable
scale.
The area enclosed by the boundary lines is divided into a
number of triangles and trapezoids.
The area of each segment may be computed by the
suitable formulae.
The computation of the areas should be written in the
tabular form.

7. Computation of Area
'area' in the context of surveying refers to the area of a
tract of land projected upon the horizontal plane, and
not to the actual area of the land.
Area may be expressed as
I. Square metres
2. Hectares (1 hectare = 10,000 m2)
3. Square feet
4. Acres (1 acre = 4840 sq. yd. = 43,560 sq. ft.).

8. Computation of area from field notes
This is done in two steps.
Step 1
In cross-staff survey, the area of field can be directly
calculated from fields.
During survey work the whole area is divided into
some geometrical figures, such as triangles, squares
and trapeziums, and then the area is calculated.
Step 2
The area along the boundaries is calculated.

9. Computation of area from field notes
1. Area of triangle
Where a, b and c are the sides, and
• Area of triangle A= 1/2 x b x h
Where b = base h = altitude
2. Area of rectangle A= a x b
where a and b are the sides.
3. Area of square = a2
where a is the side of the square.
4. Area of trapezium A= 1/2 (a + b) x d
where a and b are the parallel sides, and d is the
perpendicular distance between them.

10. Problem 1
The following is a sample chainage reading of a chain
survey. Draw a map based on chainage reading and
Calculate the area of the field using tabular method.

11. Problem – 1 – Solution
Draw a map based on the chainage reading given below

12. Problem – 1 – Solution
S.
No.
(1)
Figure
(2)
Chainage
(m)
(3)
Base
length
(m)
(4)
Offsets
(m)
(5)
Mean
offset
(m)
(6)
Area
(m2)
(6) x (4)
1 ∆ACG 0 and 20 20 0 and 42 (0+42)/2 =
21
420
2 Trap.GCEI 20 and 65 45 42 and 58 50 2250
3 ∆IEB 65 and 110 45 58 and 0 29 1305
4 ∆BFJ 90 and 110 20 0 and 60 30 600
5 Trap.FJHD 40 and 90 50 60 and 20 40 2000
6 ∆DHA 0 and 40 40 20 and 0 10 400
Total Area = Sum of the individual area 6975

13. Problem 2
The following is a chainage reading of a chain survey. Draw
a map based on chainage reading and Calculate the area of
the field using tabular method and triangulation method.

14. Problem 2 - Solution
A
B
C
D
E
F
G
15
30
60
88
98
20
30
22
15
14
H
I
J
K
L
D
G
15 20
30
14
60 30
88
15
98 22

15. Problem 2 - Solution

16. Problem – 2 – Solution
S. No. Figure Base length
or
Parallel side
(a)
Offset length or
perpendicular
distance
(b)
Area
(m2)
1 ∆ DHC 15 20 150
2 Trap. HJBC
3 Trap. ABJL
4 ∆ ALG
5 ∆ FKG
6 Trap. EFKI
7. ∆ EID
Total Area 3611

17. Problem 3
Plot the following cross staff survey of a field and calculate
its area (all dimensions are in m)
A
0
15
30
48
72
96
30 B
45 C
E 48
F 36
D

18. Problem 4
Plot the following oblique offset of survey of a field and
calculate its area (all dimensions are in m)
5
10
0
20
7
9
10
8
7
8 10
12
6
5

19. Problem 4
Plot the following oblique offset of survey of a field and
calculate its area (all dimensions are in m)
Area of unequal sides of triangle
Where a, b and c are the sides, and