To determine the Area of a Closed Traverse by Coordinates method.

Equipment:

Digital theodolite, tripod stand, leveling staff, ranging rods, plum bob, prismatic compass, and tape.

Procedure:

1. Mark station A then mark North with the help of a prismatic compass at station A.
2. Set the instrument at station A and done the temporary adjustment.
3. Horizontal clamp is kept fixed and the vertical clamp loosened, then set telescope at 90˚ with the help of the vertical clamp and vertical screw.
4. Now the vertical clamp is tightly fixed and horizontal clamp is loosened and telescope is directed towards north and bisect the ranging rod.
5. Horizontal clamp is fixed and set horizontal angle as 0˚ by using a reset button.
6. Now loose the horizontal clamp and the telescope is directed towards B and bisect the ranging rod at B.
7. Note the H.A. displayed at display screen, which is the bearing of line AB.
8. Then measure the distance from station A to B with the help of tape and note it in the observation table.
9. Repeat the above process for bearings and distances of lines BC, CD, DE, and EA.
10. Find the latitude by using LCosθ and departure by using LSineθ (where L is distance of the line and θ is the bearing of that line).
11. Let the coordinates of point A as (0, 0).
12. And find the coordinates of other stations by adding latitudes and departures in the coordinates of station A.
13. The coordinates are arranged in determinant form as follows.

14. Sum of products along the solid line,

∑P = (Y1.X2+Y2.X3+Y3.X4+Y4.X5+Y5.X1)

15. Sum of products along the dotted lines,

∑Q = (X1.Y2+X2.Y3+X3.Y4+X4.Y5+X5.Y1)

16. Now area is calculated by following formula, Area = 1/2 x (∑P –∑Q)

Observations

AreaCalculations

∑P = 1255.0

∑Q = -1053.7387

Area = 1/2 x (∑P –∑Q)

Area = 1/2 x (1255 – (-1053.7387)) = 1154.36 ft2