--- title: "Area by DMD, traverse ABCDEA (-5.693)" subject: "Surveying I" chapter: 9 key: "semester_3/surveying_i:dmd-five-sides-lat-minus-5-693" source: https://www.bctengineer.com/q/semester_3/surveying_i/dmd-five-sides-lat-minus-5-693 site: BCT Engineering --- # Area by DMD, traverse ABCDEA (-5.693) Surveying I · Chapter 9: Computation of Area and Volume - Asked in: 2080 Baisakh, 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-five-sides-lat-minus-5-693 - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-9 ## Question Calculate the area of the following traverse ABCDEA by double meridian distance method. | Line | AB | BC | CD | DE | EA | |---|---|---|---|---|---| | Latitude (m) | -5.693 | -21.361 | -28.201 | +1.103 | +54.242 | | Departure (m) | -33.990 | -13.911 | +18.867 | +28.608 | +0.426 | ## Short answer Using the Double Meridian Distance method with the given latitudes and departures, area = 2028.41 m² (0.2028 ha). ## Answer The latitudes sum to 0.090 m and the departures to 0.000 m. The latitude misclosure of 0.090 m is small (about 1 in 2,000 of the perimeter of about 177 m), so the given figures are used without adjustment. #### 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) = -33.990 - DMD(BC) = -33.990 + (-33.990) + (-13.911) = -81.891 - DMD(CD) = -81.891 + (-13.911) + (18.867) = -76.935 - DMD(DE) = -76.935 + (18.867) + (28.608) = -29.460 - DMD(EA) = -29.460 + (28.608) + (0.426) = -0.426 - Check: DMD(EA) = -0.426 = −D(EA) = -0.426, so the DMDs are correct. | Line | Latitude L (m) | Departure D (m) | DMD (m) | L × DMD (m²) | |---|---|---|---|---| | AB | -5.693 | -33.990 | -33.990 | 193.505 | | BC | -21.361 | -13.911 | -81.891 | 1749.274 | | CD | -28.201 | 18.867 | -76.935 | 2169.644 | | DE | 1.103 | 28.608 | -29.460 | -32.494 | | EA | 54.242 | 0.426 | -0.426 | -23.107 | | **Sum** | 0.090 | 0.000 | | **4056.821** | $$ \text{Area} = \frac{|4056.821|}{2} = 2028.411\ \text{m}^2 $$ **Answer: Area = 2028.41 m² (0.2028 ha).** (If the latitudes are first balanced by Bowditch's rule, the area changes only slightly, to about 2030 m².) ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The latitudes sum to 0.090 m. Why is the data used as given? A. Misclosure is always ignored B. The misclosure is very small compared with the perimeter C. Departures sum to zero so latitudes do not matter D. The error cancels in the DMD Answer: B. 0.090 m is negligible against the perimeter, so no correction is applied. (Key point: Misclosure) 2. How is the DMD of a line (other than the first) found? A. DMD of previous line + departure of previous line + departure of the line itself B. DMD of previous line - departure of the line itself C. Latitude of previous line + latitude of the line D. Sum of all departures Answer: A. Each DMD = previous DMD + previous departure + own departure. (Key point: DMD rule) 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. Why do many DMDs come out negative? A. Because the latitudes are negative B. Because of an arithmetic mistake C. Because the departures at the start are westward (negative), putting the meridian east of those lines D. DMDs are always negative Answer: C. The meridian is through the starting station and the first departure is negative, so early DMDs are negative; only the absolute value of the final sum is used. (Key point: Sign of 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 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× ## 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× - [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× - [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 - [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 - [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 AB and EA from latitudes, departures](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alatitude-departure-bearings-ab-ea) — Surveying II, chapter 1 - [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 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×