What check is available on the DMDs?

The DMD of the last line equals its departure with opposite sign

The first and last DMDs are equal

The last DMD equals the last latitude

How is the area obtained from the DMD table?

1/2 x |sum of (latitude x DMD)|

Short answer

DMDs: 405.85, 811.70, 660.15, 360.50, 106.20 m; Σ(L×DMD) = 155128.97 m². Area = 77564.49 m² (7.7564 ha).

Compute the area of the following traverse by DMD method.

The traverse closes: ΣL = 0.00 and ΣD = 0.00.

DMD rule (taking the meridian through the starting station):

DMD of the first line = departure of the first line.
DMD of any line = DMD of the previous line + departure of the previous line + departure of the line itself.
DMD of the last line = departure of the last line with opposite sign (a check).
Double area = Σ (latitude × DMD), and area = ½ |Σ L × DMD|.
DMD(AB) = D(AB) = 405.85
DMD(BC) = 405.85 + (405.85) + (0.00) = 811.70
DMD(CD) = 811.70 + (0.00) + (-151.55) = 660.15
DMD(DE) = 660.15 + (-151.55) + (-148.10) = 360.50
DMD(EA) = 360.50 + (-148.10) + (-106.20) = 106.20
Check: DMD(EA) = 106.20 = −D(EA) = 106.20, so the DMDs are correct.

Line	Latitude L (m)	Departure D (m)	DMD (m)	L × DMD (m²)
AB	0.00	405.85	405.85	0.00
BC	182.00	0.00	811.70	147729.40
CD	87.50	-151.55	660.15	57763.13
DE	-85.50	-148.10	360.50	-30822.75
EA	-184.00	-106.20	106.20	-19540.80
Sum	0.00	0.00		155128.97

\text{Area} = \frac{|155128.97|}{2} = 77564.49\ \text{m}^2

Answer: Area = 77564.49 m² (7.7564 ha).

✓ Answer checked by Claude Opus 5.5 (high effort)