Theodolite surveying

Royal University of Bhutan
Jigme Namgyel Engineering College
Department of Civil Engineering & Surveying
Tutor : Phurba Tamang
Designation: Associate lecturer
Department of Civil Engineering and Surveying
Theodolite Surveying
MODULE: SURVEYING
Spring Semester 2020

MID-TERM REVIEW, 2017
UNIT 4: Theodolite Surveying
Introduction to Theodolite
Theodolite is a very useful instrument for engineers. It is used primarily for measuring horizontal
and vertical angles. However the instrument can be used for other purposes like prolonging a line,
measuring distances indirectly and levelling.
Theodolite these days are all transit theodolites. Here the line of sight can be rotated in a vertical
plane through 180 degrees about its horizontal axis. This is known as transiting and thus the name
‘transit’ is derived.
Theodolite Traversing
Traversing is that type of survey in which member of connected survey line form the frame work
and the direction and lengths of the survey lines are measured with help of an angle measuring
instrument. Theodolite traversing is a method of establishing control points and their position
being determined by measuring distance between the traverse station and angle subtended at the
various station by their adjacent stations. After measuring angle, length and direction, Gales table
is prepared to calculate final traversing. Gales table helps in calculating errors and getting
accurate bearings, angles and lengths

Components of Theodolite

List of Equipment for Theodolite Traversing
• Theodolite
• Ranging rod
• Tripod Stand
• Plumb bob
• Measuring Tape
• Pegs
Plumb bob
Theodolite
with tripod
stand
Ranging Rods
Wooden Pegs
Measuring Tape

Theodolite Adjustments
A. Setting, Levelling and Centering Theodolite
• Release the clamp screw of the instrument
• Hold the instrument in the right hand and fix it on the tripod by turning round only the lower part with the
left hand.
• Screw the instrument firmly and bring all the foot screws to the center of its run.
• Spread the tripod legs well apart and fix any two legs firmly into the ground by pressing them with the
hand.
• Move the third leg to up or down until the main bubble is approximately in the center.
• Then move the third leg in or out until the bubbles of the cross-level is approximately in the center.
• Fix the third leg firmly when the bubbles are approximately in the centers of their run.
• Place the telescope parallel to a pair of foot screws.
• Bring the bubble to the center of its run by turning the foot screws equally either both inwards and both
outwards.
• Turn the telescope through 90 degrees , so that it lies over the third foot screw.
• Turn this third foot screw so that the bubble comes to the center of its run.
• Turn the telescope through and check whether the bubble remains central
• Looking through the optical plummet, focus the centering index mark. Slide the theodolite on the tripod
head until the reference mark is centered in the optical plummet.
• Fully tighten the centering screw. Look through the optical plummet again and adjust the theodolite foot
screws for alignment with the reference mark.

B. Instructions for Theodolite Traversing
• The area to be surveyed is first thoroughly examined to decide the best possible way of starting the work.
• Consider a closed traverse with stations namely ABCDEFA. The traverse stations are marked on the ground
by wooden pegs with nails on top.
• Set up the instrument at A. Complete the adjustments (levelling and centering) before sighting the station B.
• Once levelling and centering have been achieved, turn on the theodolite by pressing the power key.
• Place the compass over the theodolite and rotate to find the direction of meridian (North).
• Once the direction has be set, press the HOLD key twice to lock the reference direction.
• Press the L/R key for horizontal angle options. R mode is used when the traversing is carried out in
clockwise direction and L mode in counter-clockwise direction.
• Press V/% key to see the inclination angle of optical telescope. The angle has to be in 000’0’’ (zero
inclination) to maintain the line of collimation throughout the process of traversing.
• After zero-inclination has been maintained, use the vertical clamp screw to restrict the rotation of
telescope.
• Now, sight the levelling staff or ranging rod placed at B and record the fore bearing.
• Station the instrument at Station B and sight at Station A and record its back bearing.
• Similarly, complete the process for entire traverse stations.
• Find the included angles ∠A, ∠B, ∠C, ∠D, ∠E, and ∠F. Measure the length of traverse legs connecting all the
stations.
• Plot the traverse and find the closing error graphically ( Draft in AutoCAD )

• Check the adjustment of interior angles using the condition, i.e. the sum of the included angles should be
(2n±4) x 90 degrees , where n is the number of sides of closed traverse.
• Perform all essential checks using the Gale’s Traverse Table.
• Re-plot the corrected traverse.

Traverse Survey and Computations
Introduction
• A traverse is a series of connected lines whose lengths and directions are measured in the field. The
surveying performed to evaluate such field measurements is known as traversing.
• A traverse is of two types, open and closed.
Open Traverse: An open traverse is one that does not return to the starting point. It consist of a series of lines
expanding in the same direction. An open traverse cannot be checked and adjusted accurately. It is employed
for surveying long narrow strips of country, e.g. the path of a highway, railway, canal, pipeline, transmission
lines, etc.
• Closed Traverse: A traverse is said to be a closed one if it returns to the starting point, thereby forming a
closed polygon. In addition, a traverse which begins and ends at the points whose positions on the plan is
known are also referred to as a closed traverse. A closed traverse is employed for locating the boundaries
of lakes and woods, for area determination, control for mapping g and for surveying moderately large
areas.
Common uses of traversing
• To determine existing boundary lines, to calculate area within the boundary, to establish control points for
mapping and also for photogrammetric work, to establish control points for calculating earth work
quantities, for locating control points for railroads highways and other construction work.

S
Traverse Survey and Computations
CA
B D
E
F
( Open Traverse ) An open traverse terminates at a point of unknown position
A
B D
E
F
C
F ’
( Known Point )
A ’ ( Known Point )
A
D
C
B
E
F
( Closed Traverse ) A closed traverse terminates at a point of known location.

Measurement of Traverse Angles
1. Interior Angles
Interior angles of a closed traverse should be measured either clockwise or anticlockwise.
Clockwise measurement of angles is always recommended.
A
B
E
C
D

2. Deflection Angles
Open traverse, e.g. route surveys are usually run by deflection angles or angles to the right. A
deflection angle is formed at a traverse station by an extension of the previous line and the
succeeding one. The numerical value of a deflection angle must be always followed by R or L to
indicate whether it was turned right or left from the previous traverse line extended.
A
B
C
D
E
F
R R
L L

3. Angles to the Right
Angles measured clockwise from a backsight on the previous line are called angles to the right or
azimuths from the backline. This can be used in both open or closed traverse. Rotation should
always be clockwise from the backsight.
A
B
C
D
E

4. Azimuth Angles
A traverse can be run by reading azimuth angles directly. Azimuths are measured clockwise from
the north end of the meridian through the angle points. At each station the transit is to be oriented
by sighting the previous station with the back azimuth of the line as the scale readings.
N N
N N
A
B
C
Suppose the Azimuth of AB is . The azimuth of BA is160029′20′′ 340029′20′′

Latitude and Departure
Latitude of a line is the distance measured parallel to the North South Line.
Departure of a line is the distance measured parallel to the East West Line.
N
EW
S
θ
θ
L sin θ
L cos θ
L sin θ ( Departure )
L cos θ ( Latitude )
Note: Theodolite traverse is not plotted according to interior angles or bearings. It is plotted by computing
the latitudes and departures of the points and then finding the independent coordinates of the points.

The latitude and departure of lines are also expressed in the following ways:
• Northing = Latitude towards North = +L
• Southing = Latitude towards South = -L
• Easting = Departure towards East = +D
• Westing = Departure towards West = -D
Check for Closed Traverse:
1. The algebraic sum of latitudes must be equal to zero
2. The algebraic sum of departures mush be equal to zero
Line Length ( L ) Reduced Bearing (θ ) Latitude ( L cos θ ) Departure ( L sin θ )
AB L N θ E + L cos θ + L sin θ
BC L S θ E - L cos θ + L sin θ
CD L S θ W - L cos θ - L sin θ
DA L N θ W + L cos θ - L sin θ

Check for Closed Traverse:
1. Sum of Northings = Sum of Southings
2. Sum of eastings = Sum of Westings
Line Length
( L )
Reduced Bearing
(θ )
Northing ( + ) Southing ( - ) Easting ( + ) Westing ( - )
AB L N θ E L cos θ L sin θ
BC L S θ E L cos θ L sin θ
CD L S θ W L sin θ L sin θ
DA L N θ W L cos θ L sin θ

Balancing of Traverses
In case of a closed travers, the algebraic sum of latitudes must be equal to zero and that of
departures must also be equal to zero in the dial conditions. In other words, the sum of northings
must be equal to that of the southings, and the sum of the eastings must be the as that of the
westings. In actual practice some closing error is always found to exist while computing the
latitude and departures of the traverse stations. The total errors in latitude and departure are
determined. These errors are then distributed among the traverse stations proportionately.
Closing Errors:
The errors in field measurements of angles and lengths sometimes results in improper closure of
the traverse ( End point does not coincide with the starting point ). The distance by which a traverse
fails to close is known as closing error or error of closure.
Closing Error = σ 𝐿 2 + σ 𝐷 2 where, L = Latitude and D = Departure
Relative Closing Error = Closing Error / Perimeter of traverse.
Permissible Angular Error = least count x 𝑁, where N = Number of sides
tan 𝜃 =
σ 𝐷
σ 𝐿
= where θ indicates the direction of closing error.

S
Traverse for Permissible Angular Error Permissible relative closing error
1. Land, roads and railway surveys 1’ x 𝑁 1 in 3000
2. City survey, important foundry survey 30’’ x 𝑁 1 in 5000
3. Very Important Survey 15’’ x 𝑁 1 in 10000
A
B
D
C
E
F
Closing Error
σ𝐿
σ𝐷

In actual practice some closing error is always found to exist while computing the latitude and
departures of the traverse stations. The total errors in latitude and departure are determined.
These errors are then distributed among the traverse stations proportionately. The following rules
are used to distribute the errors proportionately.
1. Bowditch’s Rule
By this rule, the total error in latitude and departure is distributed in proportion to the lengths of the
traverse legs. This is the most common method of traverse adjustment.
a) Correction to latitude of any side =
𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒕𝒉𝒂𝒕 𝒔𝒊𝒅𝒆
𝑷𝒆𝒓𝒊𝒎𝒆𝒕𝒆𝒓 𝒐𝒇 𝒕𝒓𝒂𝒗𝒆𝒓𝒔𝒆
× 𝐭𝐨𝐭𝐚𝐥 𝐞𝐫𝐫𝐨𝐫 𝐢𝐧 𝐥𝐚𝐭𝐢𝐭𝐮𝐝𝐞
b) Correction to departure of any side =
𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒕𝒉𝒂𝒕 𝒔𝒊𝒅𝒆
𝑷𝒆𝒓𝒊𝒎𝒆𝒕𝒆𝒓 𝒐𝒇 𝒕𝒓𝒂𝒗𝒆𝒓𝒔𝒆
× 𝐭𝐨𝐭𝐚𝐥 𝐞𝐫𝐫𝐨𝐫 𝐢𝐧 𝐝𝐞𝐩𝐚𝐫𝐭𝐮𝐫𝐞

2. Transit Rule
a) Correction to latitude of any side =
𝑳𝒂𝒕𝒊𝒕𝒖𝒅𝒆 𝒐𝒇 𝒕𝒉𝒂𝒕 𝒔𝒊𝒅𝒆
𝑨𝒓𝒊𝒕𝒉𝒎𝒆𝒕𝒊𝒄 𝑺𝒖𝒎 𝒐𝒇 𝒂𝒍𝒍 𝒍𝒂𝒕𝒊𝒕𝒖𝒅𝒆𝒔
× 𝐭𝐨𝐭𝐚𝐥 𝐞𝐫𝐫𝐨𝐫 𝐢𝐧 𝐥𝐚𝐭𝐢𝐭𝐮𝐝𝐞
b) Correction to departure of any side =
𝑫𝒆𝒑𝒂𝒓𝒕𝒖𝒓𝒆 𝒐𝒇 𝒕𝒉𝒂𝒕 𝒔𝒊𝒅𝒆
𝑨𝒓𝒊𝒕𝒉𝒎𝒆𝒕𝒊𝒄 𝑺𝒖𝒎 𝒐𝒇 𝒂𝒍𝒍 𝒅𝒆𝒑𝒂𝒓𝒕𝒖𝒓𝒆𝒔
× 𝐭𝐨𝐭𝐚𝐥 𝐞𝐫𝐫𝐨𝐫 𝐢𝐧 𝐝𝐞𝐩𝐚𝐫𝐭𝐮𝐫𝐞
3. Third Rule
a) Correction to northing of any side =
𝑵𝒐𝒓𝒕𝒉𝒊𝒏𝒈 𝒐𝒇 𝒕𝒉𝒂𝒕 𝑺𝒊𝒅𝒆
𝑺𝒖𝒎 𝒐𝒇 𝑵𝒐𝒓𝒕𝒉𝒊𝒏𝒈
×
𝟏
𝟐
( 𝐓𝐨𝐭𝐚𝐥 𝐄𝐫𝐫𝐨𝐫 𝐢𝐧 𝐋𝐚𝐭𝐢𝐭𝐮𝐝𝐞 )
b) Correction to southing of any side =
𝑺𝒐𝒖𝒕𝒉𝒊𝒏𝒈 𝒐𝒇 𝒕𝒉𝒂𝒕 𝑺𝒊𝒅𝒆
𝑺𝒖𝒎 𝒐𝒇 𝑺𝒐𝒖𝒕𝒉𝒊𝒏𝒈
×
𝟏
𝟐
( 𝐓𝐨𝐭𝐚𝐥 𝐄𝐫𝐫𝐨𝐫 𝐢𝐧 𝐋𝐚𝐭𝐢𝐭𝐮𝐝𝐞 )
c) Correction to easting of any side =
𝑬𝒂𝒔𝒕𝒊𝒏𝒈 𝒐𝒇 𝒕𝒉𝒂𝒕 𝑺𝒊𝒅𝒆
𝑺𝒖𝒎 𝒐𝒇 𝑬𝒂𝒔𝒕𝒊𝒏𝒈
×
𝟏
𝟐
( 𝐓𝐨𝐭𝐚𝐥 𝐄𝐫𝐫𝐨𝐫 𝐢𝐧 𝐃𝐞𝐩𝐚𝐫𝐭𝐮𝐫𝐞 )
d) Correction to westing of any side =
𝑾𝒆𝒔𝒕𝒊𝒏𝒈 𝒐𝒇 𝒕𝒉𝒂𝒕 𝑺𝒊𝒅𝒆
𝑺𝒖𝒎 𝒐𝒇 𝑾𝒆𝒔𝒕𝒊𝒏𝒈
×
𝟏
𝟐
( 𝐓𝐨𝐭𝐚𝐥 𝐄𝐫𝐫𝐨𝐫 𝐢𝐧 𝐃𝐞𝐩𝐚𝐫𝐭𝐮𝐫𝐞 )
Note: If the error is positive, correction will be negative and vice vera

Balancing of Traverses ( Bowditch’s Rule )
Note: If the error is positive, correction will be negative and vice vera
Line Length
Consecutive Coordinates Correction
Corrected Consecutive
Coordinates
Latitude Departure Latitude Departure Latitude Departure
AB 70 +21.500 -65.450 +0.072 -0.064 +21.572 -65.514
BC 80 -80.755 -5.250 +0.083 -0.073 -80.672 -5.323
CD 43 -41.000 +13.550 +0.044 -0.039 -40.956 +13.511
DE 38 -14.250 +35.150 +0.038 -0.034 -14.212 +35.116
EA 115 +114.150 +22.315 +0.118 -0.105 +114.268 +22.210
Total 346 -0.355 +0.315 +0.315 -0.315 0 0
Perimeter Error Correction Adjusted

Balancing of Traverses ( Third Rule)
Note: Round up to 3 decimal places ( Ex: 3.1285 will be represented as 3.129 and 3.1284 will be 3.128 )
Line Length
Consecutive Coordinates Correction to Corrected Consecutive Coordinates
Northing
+
Southing
-
Easting
+
Westing
-
Northing Southing Easting Westing Northing
+
Southing
-
Easting
+
Westing
-
AB 70 31.500 65.45 +0.029 +0.146 21.529 65.596
BC 80 80.755 5.250 -0.106 +0.012 80.650 5.262
CD 43 41.000 13.550 -0.053 -0.030 40.947 13.520
DE 38 14.250 35.150 -0.019 -0.078 14.231 35.072
EA 115 114.150 22.315 +0.149 -0.049 114.299 22.266
Total 346 135.650 136.005 71.015 70.700 +0.178 -0.178 -0.157 +0.158 135.828 135.828 70.858 70.858
Perimeter = 346 Error = -0.355 Error = +0.315 Error = 0.000 Error = 0.000

D
Determination of Included Angles from Bearings
The included angle between two lines may either be interior or exterior angles. When traversing is
done anticlockwise, the included angles are interior, whereas in the case of clockwise traverse,
these are the exterior ones. These are always measured clockwise from the preceding line to the
forward line.
Example: Determine the value of included angles in a closed traverse ABCD conducted in clockwise
direction, given the following fore bearings of the respective lines.
LINE Fore Bearing
AB 40 °
BC 70 °
CD 210 °
DA 280 °

D

D
Since, the traversing is for this example is carried out in clockwise direction, the included angles are thus taken
as exterior angles.
Check:
Theoretical Sum of Included ( Exterior angles ) = ( 2 n + 4 ) x 90° = ( 2 x 4 + 4 ) x 90 = 1080 °
Also, sum of calculated included angles = ∠A+∠B+∠C+∠D = 300° + 210° + 320° + 250° = 1080°

D
Alternative
If interior angles are taken as include angles ( Usual
Method ), then the following check can be performed
Check:
Theoretical Sum of Included ( Interior Angles)
= ( 2 n - 4 ) x 90° = ( 2 x 4 - 4 ) x 90 = 360 °
Also, sum of calculated included angles
= ∠A+∠B+∠C+∠D = 60° + 150° + 40° + 110° = 360 °

D
Practice Example:
Following are the bearings taken in a closed traverse
LINE Fore Bearing Back Bearing
AB 142 ° 30 ′ 322 ° 30’
BC 223 ° 15 ′ 44 ° 15 ′
CD 287 ° 00 ′ 107 ° 45 ′
DE 12 ° 45 ′ 193 ° 15 ′
EA 60 ° 00 ‘ 239 ° 00 ‘
Solution:
∠A = 263 ° 30 ‘ , ∠B = 260 ° 45’ , ∠C = 242 ° 45 ‘ , ∠D = 265 ° 00 ‘ , ∠E = 226 ° 45 ‘

D
Gale’s Traverse Table
Traverse Computations are usually done in a tabular form. One such form is Gale’s Traverse table which is
widely used because of its simplicity.
Station
Line
Length
Interiorangles
Corrections
Correctedangles
WCB
RB
Quadrants
Consecutive
coordinates
Correction
(Bowditch Rule)
Corrected
Consecutive
Coordinates
Independent
Coordinates
Lat. Dep. Lat. Dep. Lat. Dep. N (+) S (-) E (+) W (-)
N (+) S (-) E (+) W (-) (+) (-) (+) (-) N (+) S (-) E (+) W (-)
A
AB
B
BC
C
CD
D
DA
A
Total Error in
Latitude =
Total Error in
Departure =

D
The following steps are involved in Theodolite Traversing
1. In the case of theodolite traversing, the included angles are adjusted to satisfy the geometrical
conditions, i.e. the sum of the included angles should be ( 2 n ± 4 ) x 90° , where n is the
number of sides of the closed traverse. The plus sign is used when the angles are exterior
angles and the minus sign when they are interior angles.
2. From the observed bearing of a line, the whole circle bearings of all other lines are calculated
and then these bearings are reduced to those in the quadrantal system.
3. From the lengths and computed reduced bearings of the lines, the consecutive coordinates i.e.
latitudes and departures are worked out.
4. A check is performed to find out whether the algebraic sum of latitudes and the algebraic sum
of departures are zero. If not a correction is applied using the transit rule.
5. The independent coordinates are then worked out from the consecutive coordinates. The origin
is so selected that the entire traverse lies in the north east quadrant. This is done to facilitate
plotting of the traverse on a sheet with the left hand bottom corner of the sheet as the origin.

D
Angle Observed Value Side Measured Length ( m )
DAB 97 ° 41 ′ AB 22.11
ABC 99 ° 53 ′ BC 58.34
BCD 72 ° 23 ′ CD 39.97
CDA 89 ° 59 ′ DA 52.10
Example: The mean observed internal angles and measured sides of a closed traverse ABCDA ( in
anticlockwise order ) area as follow:
Adjust the angles, compute the latitudes and departures assuming that D is due North of A, adjust
the traverse by the Bowditch method; and give the coordinates of B, C and D relative to A. Asses the
accuracy of these observations and justify your assessment.

D
Solution:

D
Calculation of Traverse Area
The are of a closed traverse may be calculated from
A. The coordinate ( x and y )
B. The departure and total latitudes.
A. Calculation of Area from Coordinates
The given consecutive coordinates of a traverse are
converted into independent coordinates with
reference to the coordinates of the most westerly
station. Thus, the whole traverse is transferred to
the first quadrant. From the figure, point A is the
most westerly station.
Then, the coordinates are arranged in determinant form as follows.

D
The sum of the products of coordinates joined by solid lines,
The sum of the products of coordinates joined by dotted lines,

D
Example: Find the area of the closed traverse using the coordinate method.
Side Latitude Departure
AB +225.5 +120.5
BC -245.0 +210.0
CD -150.5 -110.5
DA +170.0 -220.0
Solution:
Station Side Consecutive Coordinates Independent Coordinates
Latitude ( y ) Departure ( x ) Latitude ( y ) Departure ( x )
A +200.00 +100.00
B AB +225.5 +120.5 +425.50 +220.50
C BC -245.0 +210.0 +180.50 +430.50
D CD -150.5 -110.5 +30.00 +320.00
A DA +170.0 -220.0 +200.00 +100.00
The independent coordinates of the most westerly station A are assumed to be +200.00 , +100.00

D
Station Side Consecutive Coordinates Independent Coordinates
Latitude ( y ) Departure ( x ) Latitude ( y ) Departure ( x )
A +200.00, y1 +100.00, x1
B AB +225.5 +120.5 +425.50, y2 +220.50, x2
C BC -245.0 +210.0 +180.50, y3 +430.50, x3
D CD -150.5 -110.5 +30.00, y4 +320.00, x4
A DA +170.0 -220.0 +200.00, y5 +100.00, x5
The independent coordinates are arranged in a determinant form as follows:

D
Sum of products of coordinates joined by solid lines:
Ʃ P = ( 200.00 x 220.5 + 425.50 x 430.50 + 180.50 x 320.00 + 30.00 x 100.00 ) = 288037.75
Sum of products of coordinates joined by dotted lines:
Ʃ Q = ( 100.00 x 425.50 + 220.50 x 180.50 + 430.50 x 30.00+ 320.00 x 200.00 ) = 159265.25
Required Area, A = 0.5 x ( Ʃ P – Ʃ Q ) = 0.5 x ( 288037.75 – 159265.25 )
= 64386.25 m2

D
B. Calculation of Area from Departure and Total Latitude
Considering the following figure, point A is the most westerly station, and the reference meridian is
assume to pass through it.

D
Procedure for Calculation Area:
1. The total latitude ( the latitude with respect to the reference point ) of each station of the
traverse is found out.
2. The algebraic sum of departures of the two lines meeting at a station is determined.
3. The total latitude is multiplied by the algebraic sum of departure, for each individual point.
4. The algebraic sum of this product gives twice the area.
5. Half of this sum gives the required area.

D
Example: Find the area of the closed traverse using the departure and total latitude method.
Side Latitude Departure
AB +225.5 +120.5
BC -245.0 +210.0
CD -150.5 -110.5
DA +170.0 -220.0
The latitudes of the stations are calculated with reference to station A.
Total Latitude of B = + 225.50
Total Latitude of C = + 225.5 - 245.0 = -19.5
Total Latitude of D = + 225.50 – 245.0 – 150.5 = - 170.0
Total Latitude of A = + 225.5 – 245.0 – 150.5 + 170.0 = 0.0

D
Algebraic sum of departures at B = AB + BC = 120.5 + 210.0 = + 330.5
Algebraic sum of departures at C = BC + CD = + 210.0 – 110.5 = + 99.5
Algebraic sum of departures at D = CD + DA = - 110.5 – 220.0 = - 330.5
Algebraic sum of departures at A = DA + AB = - 220.0 + 120.5 = - 99.5
The result is tabulated as follows:
Side Latitude Departure Station Total
Latitude
Algebraic
Sum of
adjoining
Departure
Double Area
Column 5 x Column 6
+ -
1 2 3 4 5 6 7 8
AB +225.5 +120.5 B + 225.50 + 330.50 74527.75
BC -245.0 +210.0 C - 19.50 + 99.50 _____ 1940.25
CD -150.5 -110.5 D - 170.00 - 330.50 56185.00 _____
DA +170.0 -220.0 A 0.00 - 99.50 _____ 0.00
Total +130712.75 – 1940.25
Algebraic Sum = +128772.50
Twice Area = Algebraic Sum of Column 7 and 8= +128772.50
Required Area = 0.5 x 128772.50 = 64386.25 𝑚2

Theodolite surveying

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