--- title: "Area by DMD, departure AB 405.85" subject: "Surveying I" chapter: 9 key: "semester_3/surveying_i:dmd-traverse-ab-405-85" source: https://www.bctengineer.com/q/semester_3/surveying_i/dmd-traverse-ab-405-85 site: BCT Engineering --- # Area by DMD, departure AB 405.85 Surveying I · Chapter 9: Computation of Area and Volume - Asked in: 2078 Kartik, 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-405-85 - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-9 ## Question Compute the area of the following traverse by DMD method. | Line | Latitude (m) | Departure (m) | |---|---|---| | AB | 0.00 | 405.85 | | BC | 182.00 | 0.00 | | CD | 87.50 | -151.55 | | DE | -85.50 | -148.10 | | EA | -184.00 | -106.20 | ## Short answer DMDs: 405.85, 811.70, 660.15, 360.50, 106.20 m; Σ(L×DMD) = 155128.97 m². Area = 77564.49 m² (7.7564 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) = 405.85 - DMD(BC) = 405.85 + (405.85) + (0.00) = 811.70 - DMD(CD) = 811.70 + (0.00) + (-151.55) = 660.15 - DMD(DE) = 660.15 + (-151.55) + (-148.10) = 360.50 - DMD(EA) = 360.50 + (-148.10) + (-106.20) = 106.20 - Check: DMD(EA) = 106.20 = −D(EA) = 106.20, so the DMDs are correct. | Line | Latitude L (m) | Departure D (m) | DMD (m) | L × DMD (m²) | |---|---|---|---|---| | AB | 0.00 | 405.85 | 405.85 | 0.00 | | BC | 182.00 | 0.00 | 811.70 | 147729.40 | | CD | 87.50 | -151.55 | 660.15 | 57763.13 | | DE | -85.50 | -148.10 | 360.50 | -30822.75 | | EA | -184.00 | -106.20 | 106.20 | -19540.80 | | **Sum** | 0.00 | 0.00 | | **155128.97** | $$ \text{Area} = \frac{|155128.97|}{2} = 77564.49\ \text{m}^2 $$ **Answer: Area = 77564.49 m² (7.7564 ha).** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is DMD(AB) for the first line? A. Zero B. Equal to its departure, 405.85 C. Its latitude D. Twice its departure Answer: B. The first line DMD equals its own departure when the meridian passes through the start station. (Key point: First DMD) 2. BC has departure 0.00. What is DMD(BC)? A. 811.70 B. 405.85 C. 0.00 D. 1217.55 Answer: A. 405.85 + 405.85 + 0 = 811.70. (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. 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 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× ## 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 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 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× - [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× - [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 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 ## Related in other subjects - [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 - [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× - [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 - [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×