To calculate the area of the garden plot, we can use the Shoelace Theorem (also known as Gauss's area formula). This formula helps us find the area of a polygon when the vertices are given as coordinates.

Coordinates of the poles:

1. First pole: $(0, 0)$
2. Second pole: $(6, 0)$
3. Third pole: $(4, 5)$
4. Fourth pole: $(2, 4)$

The Shoelace Theorem states that if the vertices of the polygon are given by $(x_1, y_1), (x_2, y_2), \dots, (x_n, y_n)$, the area is calculated as:

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

Let's apply the coordinates of the garden plot to this formula.

Step-by-step calculation:

1. Write the coordinates, repeating the first coordinate at the end to close the loop: $(0, 0), (6, 0), (4, 5), (2, 4), (0, 0)$

2. Multiply the coordinates in a specific order (cross-multiplication): $\text{Sum 1} = (0 \times 0) + (6 \times 5) + (4 \times 4) + (2 \times 0) = 0 + 30 + 16 + 0 = 46$ $\text{Sum 2} = (0 \times 6) + (0 \times 4) + (5 \times 2) + (4 \times 0) = 0 + 0 + 10 + 0 = 10$

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

4. Now, divide by 2 to get the area: $A = \frac{1}{2} \times 36 = 18$

Conclusion:

The total area of the garden plot is 18 square feet.

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Would you like further details on the Shoelace Theorem or have any questions about this problem?

Here are some related questions:

1. How do you apply the Shoelace Theorem to a triangle?
2. What if the coordinates were in a different order?
3. Can the Shoelace Theorem be used for irregular polygons?
4. How do you calculate the area of a garden plot if it has more than four poles?
5. Can you use the Shoelace Theorem for three-dimensional shapes?

Tip: Double-check the coordinates to ensure you close the loop (i.e., repeat the first point as the last one).