Area of traverse by DMD and coordinates (N/S/E/W)

Convert the table to signed values (N and E positive, S and W negative): ΣN = 123 = ΣS and ΣE = 257 = ΣW, so the traverse closes.

DMD method

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) = 4

• DMD(BC) = 4 + (4) + (249) = 257

• DMD(CD) = 257 + (249) + (4) = 510

• DMD(DA) = 510 + (4) + (-257) = 257

• Check: DMD(DA) = 257 = −D(DA) = 257, so the DMDs are correct.

$$\text{Area} = \frac{|-58443|}{2} = 29221.5\ \text{m}^2$$

Coordinate method

Taking the first station as the origin (N = 0, E = 0) and adding the latitudes and departures successively gives the total coordinates. The area is

$$2A = \sum N_i\,(E_{i+1} - E_{i-1})$$ $$\text{Area} = \frac{|58443|}{2} = 29221.5\ \text{m}^2$$

Both methods agree.

Answer: Area = 29221.50 m² (2.922 ha).