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To solve this problem, we are asked to calculate the area of a closed traverse using two methods: the **Co-ordinates Method** and the **Meridian Distance Method**. 

### Step 1: Understanding the traverse and data

We are given a table that describes the lines of the closed traverse with their northings, southings, eastings, and westings:

| Line | Northing | Southing | Easting | Westing |
|------|----------|----------|---------|---------|
| AB   | -        | 157.20   | 154.80  | -       |
| BC   | 210.50   | -        | -       | 52.50   |
| CD   | 175.40   | -        | 98.30   | -       |
| DA   | -        | 228.70   | -       | 109.00  |

For the **Coordinate Method**, the key step is to calculate the coordinates of the vertices using the latitudes (northings and southings) and departures (eastings and westings) and then use the formula to calculate the area.

For the **Meridian Distance Method**, the key steps involve calculating the meridian distances (i.e., half-sum of consecutive easting values) and then using them to compute the area.

Let me go ahead and compute the area for you using these methods.Using the **Coordinates Method**, the area of the traverse is approximately **21,803.35 square units**.

Next, I will calculate the area using the **Meridian Distance Method**, which involves calculating meridian distances and applying the formula for traverse area. Let me compute that for you.It seems like I can’t do more advanced data analysis right now. Please try again later. 

However, based on the calculation for the **Coordinates Method**, the area is approximately **21,803.35 square units**. You can use this result while I fix the issue for the **Meridian Distance Method**.

Would you like me to provide more details on the coordinate method or any further clarifications? Also, here are 5 related questions for expanding your understanding:

1. How do we handle traverse data with missing or incomplete latitude/longitude values?
2. What are the main differences between the Coordinate and Meridian Distance methods?
3. How can errors in field data affect the traverse area calculation?
4. What are some other methods for calculating the area of a closed traverse?
5. How do we adjust for misclosure errors in a traverse?

**Tip**: Always ensure that your latitudes (northings and southings) and departures (eastings and westings) balance in a closed traverse to minimize errors.

The latitude and departures of the lines of a closed traverse are given. Calculate the area of traverse by Co-ordinates method and Meridian distance method.

Learn how to calculate the area of a closed traverse using the Coordinates Method and the Meridian Distance Method with a worked example. Suitable for students in surveying or civil engineering courses.

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