---
title: "Area by DMD, traverse ABCDE (+218)"
subject: "Surveying I"
chapter: 9
key: "semester_3/surveying_i:dmd-traverse-ab-218"
source: https://www.bctengineer.com/q/semester_3/surveying_i/dmd-traverse-ab-218
site: BCT Engineering
---

# Area by DMD, traverse ABCDE (+218)

Surveying I · Chapter 9: Computation of Area and Volume

- Asked in: 2076 Chaitra, 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-218
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-9

## Question

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

| Line | AB | BC | CD | DE | EA |
|---|---|---|---|---|---|
| Latitude (m) | +218 | -277 | -109 | -207 | +375 |
| Departure (m) | +202 | +80 | -332 | -301 | +351 |

## Short answer

DMDs: 202, 484, 232, −401, −351 m; Σ(L×DMD) = −163938 m². Area = 81969.00 m² (8.1969 ha).

## Answer

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

#### 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) = 202
- DMD(BC) = 202 + (202) + (80) = 484
- DMD(CD) = 484 + (80) + (-332) = 232
- DMD(DE) = 232 + (-332) + (-301) = -401
- DMD(EA) = -401 + (-301) + (351) = -351
- Check: DMD(EA) = -351 = −D(EA) = -351, so the DMDs are correct.

| Line | Latitude L (m) | Departure D (m) | DMD (m) | L × DMD (m²) |
|---|---|---|---|---|
| AB | 218 | 202 | 202 | 44036 |
| BC | -277 | 80 | 484 | -134068 |
| CD | -109 | -332 | 232 | -25288 |
| DE | -207 | -301 | -401 | 83007 |
| EA | 375 | 351 | -351 | -131625 |
| **Sum** | 0 | 0 | | **-163938** |

$$
\text{Area} = \frac{|-163938|}{2} = 81969\ \text{m}^2
$$

**Answer: Area = 81969.00 m² (8.1969 ha).**

## Check yourself

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

1. Why is no correction needed?
   A. Sides form a pentagon
   B. Sum of latitudes and sum of departures are both zero
   C. Departures are bigger than latitudes
   D. The area is large
   Answer: B. Closed traverse with zero sums. (Key point: Closure)

2. Departures AB = +202, BC = +80. What is DMD(BC)?
   A. 484
   B. 282
   C. 202
   D. 80
   Answer: A. 202 + 202 + 80 = 484. (Key point: DMD of BC)

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. The sum of L x DMD is -163938. What area results?
   A. -81969 m^2
   B. 163938 m^2
   C. 81969 m^2, taking half the absolute value
   D. -163938 m^2
   Answer: C. Area cannot be negative; the sign only shows direction of traverse. (Key point: Result sign)

## Close variants set in other exams

- [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×
- [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×

## Related in Surveying I

- [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×
- [Meridian distance, DMD and area calculation](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Ameridian-distance-and-dmd-area) — Surveying I, chapter 9, asked 2×
- [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 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 DMD, traverse ABCD (225.28)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Admd-traverse-ab-225-28) — Surveying I, chapter 9, asked 2×
- [Local attraction, bearings AB 305°00′ (EA 45°)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ea-305-00) — Surveying I, chapter 4, asked 2×

## Related in other subjects

- [Bearings of DE and EA in traverse ABCDE](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-abcde-bearings-de-ea) — Surveying II, chapter 1, asked 2×
- [Bearings of BC and CD in traverse ABCDE](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-abcde-bearings-bc-cd) — Surveying II, chapter 1, asked 2×
- [Traverse missing length CD, bearing EA](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-missing-cd-length-ea-bearing) — Surveying II, chapter 1
- [Closed traverse missing EA bearing, BC length](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-traverse-abcdea-missing-ea-bc) — Surveying II, chapter 1