3. Area By DMDs
a. Concept
Software uses coordinates for area determination. Most surveyors who solve area manually generally use coordinates also. A traditional method of computing area of a closed polygonal traverse is by DMDs: Double Meridian Distances. While rarely used anymore, every now and then you'll hear it mentioned so we'll spend some time going over Area by DMDs.
A meridian distance (MD) is the distance from a reference meridian to the center of a line; it is measured in the East (X) direction, Figure G10.
Figure G10 
The reference meridian used can be placed anywhere, but generally, it passes through the first point of the traverse. Triangular and trapezoidal areas can be computed by multiplying a meridian distance by the latitude of the respective line. The base of each triangle or trapezoid coincides with the meridian. Adding the areas, some of which are negative based on the latitude and meridian distance, results in the area of the polygon.
Why then the Double Meridian Distance? Well if we start at point A in Figure G10 and begin computing meridian distances, we see a pattern start to develop, Equation G4.
Equation G4 
See all those 1/2's? By multiplying both sides of each MD equation by 2, the 1/2's all go away and we're left with Double Meridian Distances (DMDs) on each left side, Equation G5.
Equation G5 
Notice that the DMD of the last line is the same as the Departure of that line except with an opposite math sign. That's the math check.
Multiplying each line's DMD by its Latitude and summing the results will give us double the area.
Equation G6 
Just like area by coordinates it looks pretty confusing, but there is a pattern that helps guide the calculations.
You'll sometimes see reference to Area by DPDs (Double Parallel Distance). This is identical to the DMD method except everything is rotated 90°. Parallel distances are determined from an E/W reference line (a parallel) and multiplied by the latitudes.
b. Examples
(1) Traverse 1
Figure G11 shows the example Bearing Traverse with the previously computed adjusted Latitudes and Departures.


Figure G11 Example DMD Traverse 
Step (1) Compute the DMDs
Starting with line AB and use Equation G4 to computed the DMDs.
If you examine the Deps and DMDs computations above, you should see a pattern to the computations. This pattern is shown using colored arrows below.
Step (2) Multiply DMDs by Lats; add the products
Adjusted  
Line  Lat (ft)  Dep (ft)  DMD (ft)  DMD x Lat (sq ft) 
AB  176.386  438.574  438.574  +77,358.3 
BC  +203.382  73.105  950.253  193,264.4 
CD  +192.340  +198.635  824.723  158,627.2 
DE  219.336  +313.044  313.044  +68,661.8 
sum: 
205,871.5 
Step (3) Compute the area using Equation G6
Note that this is the same as computed by coordinates. Surprise.
(2) Traverse 2
What about the Crossing Traverse?
Figure G12 
Figure G13 
The parcel area, Figure G12, can not be determined by DMDs without additional computations. By definition, Area by DMDs is limited to travel along the traverse path so you would be determining the area of EFGHE, Figure G13. That area doesn't make sense since the traverse crosses itself. To compute the area of the parcel by DMDs, you would need to determine the Lat and Dep of lines EF and FH, then compute DMDs around the perimeter. By the time all that was done, the area could have been computed by coordinates.