FUNDAMENTAL SURVEYING Coordinate Geometry (COGO) & Area Calculation 1 — Questions and Answers
Question 1: What does COGO stand for in surveying?
- Cartographic Operations and Geodetic Output
- Coordinate Geometry (Correct answer)
- Control Grid Operations
- Contour Generation Output
Correct answer: Coordinate Geometry
COGO (Coordinate Geometry) is the mathematical framework used to compute positions, distances, angles, and areas from coordinate data.
Question 2: What formula is used in the 'coordinate method' (shoelace formula) to compute traverse area?
- Area = 0.5 times the absolute sum of (Xn times Yn+1 minus Xn+1 times Yn) (Correct answer)
- Area = base times height divided by 2
- Area = sum of (latitude times departure)
- Area = pi times radius squared
Correct answer: Area = 0.5 times the absolute sum of (Xn times Yn+1 minus Xn+1 times Yn)
The coordinate (cross-product / shoelace) formula computes area as half the absolute value of the algebraic sum of cross-products of successive coordinates.
Question 3: A parcel has a computed area of 87,120 sq ft. How many acres is this?
- 1 acre
- 2 acres (Correct answer)
- 0.5 acre
- 4 acres
Correct answer: 2 acres
1 acre = 43,560 sq ft; 87,120 divided by 43,560 = 2 acres.
Question 4: In state plane coordinates, what is the 'scale factor'?
- The ratio used to correct ground distances to grid distances (Correct answer)
- The number of coordinate units per inch on a map
- The ratio of magnetic to true north
- The factor applied to convert feet to meters
Correct answer: The ratio used to correct ground distances to grid distances
The scale factor is a multiplier applied to ground distances to obtain grid distances on the state plane projection, varying slightly across each zone.
Question 5: What is the 'combined factor' in state plane surveying?
- Scale factor times elevation factor, used to convert ground distances to grid distances (Correct answer)
- The total area multiplied by the zone factor
- Magnetic declination plus convergence angle
- The ratio of grid area to ground area
Correct answer: Scale factor times elevation factor, used to convert ground distances to grid distances
The combined factor = scale factor times elevation (sea-level) factor, allowing direct conversion from ground distances to grid distances.
Question 6: The Double Meridian Distance (DMD) method is used to compute:
- Magnetic bearings from astronomic observations
- Area of a closed traverse using latitudes and departures (Correct answer)
- Elevation differences using trigonometry
- GPS coordinate transformations
Correct answer: Area of a closed traverse using latitudes and departures
DMD multiplies the double meridian distance of each course by its latitude and sums the products to obtain twice the traverse area.
FUNDAMENTAL SURVEYING Coordinate Geometry (COGO) & Area Calculation 1
What does COGO stand for in surveying?