---
title: "Area by DMD, traverse ABCD (225.28)"
subject: "Surveying I"
chapter: 9
key: "semester_3/surveying_i:dmd-traverse-ab-225-28"
source: https://www.bctengineer.com/q/semester_3/surveying_i/dmd-traverse-ab-225-28
site: BCT Engineering
---

# Area by DMD, traverse ABCD (225.28)

Surveying I · Chapter 9: Computation of Area and Volume

- Asked in: 2076 Asoj, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/dmd-traverse-ab-225-28
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-9

## Question

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 |

## 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).

## Answer

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

#### 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) = 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).**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is the DMD of a line (other than the first) found?
   A. DMD of previous line - departure of the line itself
   B. DMD of previous line + departure of previous line + departure of the line itself
   C. Latitude of previous line + latitude of the line
   D. Sum of all departures
   Answer: B. Each DMD = previous DMD + previous departure + own departure. (Key point: DMD rule)

2. DMD(BC) = 871.78, D(BC) = 417.26, D(CD) = -196.47. What is DMD(CD)?
   A. 1092.57
   B. 871.78
   C. 1288.80
   D. -196.47
   Answer: A. 871.78 + 417.26 - 196.47 = 1092.57. (Key point: DMD of CD)

3. What check is available on the DMDs?
   A. The sum of DMDs is zero
   B. The first and last DMDs are equal
   C. The last DMD equals the last latitude
   D. The DMD of the last line equals its departure with opposite sign
   Answer: D. With the first-line DMD starting at its departure, the last DMD must equal minus the last departure. (Key point: DMD check)

4. What area is obtained?
   A. 326035.30 m^2
   B. 81508.83 m^2
   C. 163017.65 m^2
   D. 1092.57 m^2
   Answer: C. The sum -326035.30 is halved: 163017.65 m^2. (Key point: Final area)

## Close variants set in other exams

- [Area by DMD, departure AB 405.85](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Admd-traverse-ab-405-85) — Surveying I, chapter 9, asked 2×

## Related in Surveying I

- [Area by total coordinates and DMD (AB 90.29)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Admd-and-coordinates-ab-90-29) — Surveying I, chapter 9
- [Area by coordinates and DMD (AB -370)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aarea-coordinate-and-dmd-minus-370) — Surveying I, chapter 9, asked 4×
- [Area by DMD, traverse ABCDEA (-5.693)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Admd-five-sides-lat-minus-5-693) — Surveying I, chapter 9, asked 4×
- [Area of traverse by DMD and coordinates (N/S/E/W)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aarea-closed-traverse-nswe-108) — Surveying I, chapter 9
- [Area by DMD, traverse ABCDE (+218)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Admd-traverse-ab-218) — Surveying I, chapter 9, asked 4×
- [Area by DMD, traverse PQRS](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Admd-traverse-pqrs-minus-300) — Surveying I, chapter 9, asked 4×

## Related in other subjects

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- [Hardy-Cross network discharge AB, BC, AD, CD](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ahardy-cross-as69) — Water Supply Engineering, chapter 7
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