---
title: "Area by DMD, traverse PQRS"
subject: "Surveying I"
chapter: 9
key: "semester_3/surveying_i:dmd-traverse-pqrs-minus-300"
source: https://www.bctengineer.com/q/semester_3/surveying_i/dmd-traverse-pqrs-minus-300
site: BCT Engineering
---

# Area by DMD, traverse PQRS

Surveying I · Chapter 9: Computation of Area and Volume

- Asked in: 2072 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-pqrs-minus-300
- 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 | PQ | QR | RS | SP |
|---|---|---|---|---|
| Latitude (m) | -300 | 640 | 100 | -440 |
| Departure (m) | 450 | 110 | -380 | -180 |

## Short answer

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

## Check yourself

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

1. What confirms the traverse PQRS closes?
   A. All sides equal
   B. Sum of latitudes = 0 and sum of departures = 0
   C. All angles 90 degrees
   D. Positive latitudes only
   Answer: B. Both sums are zero. (Key point: Closure)

2. With D(PQ) = 450 and D(QR) = 110, DMD(QR) is
   A. 1010
   B. 560
   C. 450
   D. 110
   Answer: A. 450 + 450 + 110 = 1010. (Key point: DMD of QR)

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. How is the area obtained from the DMD table?
   A. sum of (departure x DMD)
   B. sum of (latitude x departure)
   C. 1/2 x |sum of (latitude x DMD)|
   D. sum of DMDs divided by 2
   Answer: C. Double area = sum of latitude x DMD, so area is half its absolute value. (Key point: Area from DMD)

## Close variants set in other exams

- [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 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

- [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 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×
- [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 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×
- [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
- [Corrected bearings of closed traverse PQRST](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosed-traverse-pqrst-correct-bearings) — Surveying I, chapter 4

## Related in other subjects

- [Design pipes PQ, PR and RS, C = 110](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apd-s71) — Water Supply Engineering, chapter 7
- [Double-stub matching 110+j110 Ω on 100 Ω line](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Adouble-stub-110-j110) — RF and Microwave Engineering, chapter 2, asked 2×
- [Design main transmission pipes PQ and QR](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apd-c70o) — Water Supply Engineering, chapter 7
- [Daily PET by Penman, latitude 30 N, 300 m](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Apenman-daily-lat30-elev300) — Engineering Hydrology, chapter 3