To calculate the total area of the garden plot, we will use the shoelace theorem (or Gauss's area formula). This formula calculates the area of a polygon when its vertices are known. The formula is:

$\text{Area} = \frac{1}{2} \left| \sum_{i=1}^{n-1} (x_i y_{i+1} - y_i x_{i+1}) + (x_n y_1 - y_n x_1) \right|$

Here, the coordinates of the poles are:

1. $(0, 0)$
2. $(6, 0)$
3. $(4, 5)$
4. $(2, 4)$

To apply the shoelace theorem, we will organize the points in a list and then calculate the sum of the products of the coordinates, as shown in the formula.

The ordered vertices (in the same direction) are:

$(0, 0), (6, 0), (4, 5), (2, 4)$

Now, follow the formula step by step:

1. Multiply each x-coordinate by the y-coordinate of the next vertex (considering that after the last point, we loop back to the first): $0 \times 0 + 6 \times 5 + 4 \times 4 + 2 \times 0 = 0 + 30 + 16 + 0 = 46$

2. Multiply each y-coordinate by the x-coordinate of the next vertex (looping back to the first after the last): $0 \times 6 + 0 \times 4 + 5 \times 2 + 4 \times 0 = 0 + 0 + 10 + 0 = 10$

3. Subtract the second sum from the first sum: $46 - 10 = 36$

4. Take half of the absolute value of the result: $\text{Area} = \frac{1}{2} \times 36 = 18 \, \text{square feet}$

Thus, the total area of the garden plot is 18 square feet.

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Would you like more details or have any questions on the method used? Here's a list of further related questions:

1. How would you calculate the area of a garden plot with more vertices?
2. What is the difference between the shoelace theorem and other methods for finding area?
3. How do you apply the shoelace theorem to irregular polygons?
4. What would change if the plot had five poles instead of four?
5. Can the shoelace theorem be used for 3D polygons or shapes?

Tip: Always ensure your vertices are ordered in a consistent direction (clockwise or counterclockwise) to avoid errors in applying the shoelace theorem!