What confirms the traverse PQRS closes?

Sum of latitudes = 0 and sum of departures = 0

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

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

Short answer

DMDs: 450, 1010, 740, 180 m; Σ(L×DMD) = 506200 m². Area = 253100.00 m² (25.31 ha).

Calculate the area of the traverse by double meridian distance method.

Line	PQ	QR	RS	SP
Latitude (m)	-300	640	100	-440
Departure (m)	450	110	-380	-180

The traverse closes: ΣL = 0 and ΣD = 0.

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(PQ) = D(PQ) = 450
DMD(QR) = 450 + (450) + (110) = 1010
DMD(RS) = 1010 + (110) + (-380) = 740
DMD(SP) = 740 + (-380) + (-180) = 180
Check: DMD(SP) = 180 = −D(SP) = 180, so the DMDs are correct.

Line	Latitude L (m)	Departure D (m)	DMD (m)	L × DMD (m²)
PQ	-300	450	450	-135000
QR	640	110	1010	646400
RS	100	-380	740	74000
SP	-440	-180	180	-79200
Sum	0	0		506200

\text{Area} = \frac{|506200|}{2} = 253100\ \text{m}^2

Answer: Area = 253100.00 m² (25.3100 ha).

✓ Answer checked by Claude Opus 5.5 (high effort)