How is the DMD of a line (other than the first) found?

DMD of previous line + departure of previous line + departure of the line itself

DMD of previous line - departure of the line itself

Latitude of previous line + latitude of the line

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

Short answer

DMDs: 227.26, 871.78, 1092.57, 448.05 m; Σ(L×DMD) = −326035.30 m². Area = 163017.65 m² (16.3018 ha).

Calculate the area of the following traverse by using DMD method.

Line	AB	BC	CD	DA
Latitude (m)	225.28	-139.61	-336.90	251.23
Departure (m)	227.26	417.26	-196.47	-448.05

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) = 227.26
DMD(BC) = 227.26 + (227.26) + (417.26) = 871.78
DMD(CD) = 871.78 + (417.26) + (-196.47) = 1092.57
DMD(DA) = 1092.57 + (-196.47) + (-448.05) = 448.05
Check: DMD(DA) = 448.05 = −D(DA) = 448.05, so the DMDs are correct.

Line	Latitude L (m)	Departure D (m)	DMD (m)	L × DMD (m²)
AB	225.28	227.26	227.26	51197.13
BC	-139.61	417.26	871.78	-121709.21
CD	-336.90	-196.47	1092.57	-368086.83
DA	251.23	-448.05	448.05	112563.60
Sum	0.00	0.00		-326035.30

\text{Area} = \frac{|-326035.30|}{2} = 163017.65\ \text{m}^2

Answer: Area = 163017.65 m² (16.3018 ha).

✓ Answer checked by Claude Opus 5.5 (high effort)