To calculate the area of the garden plot formed by the four poles, we can use the shoelace theorem (also known as Gauss's area formula), which is useful for finding the area of a polygon when the coordinates of the vertices are known.

Given points:

1. Pole 1: $(0,0)$
2. Pole 2: $(6,0)$
3. Pole 3: $(94, 5)$
4. Pole 4: $(2, 4)$

To apply the shoelace formula, the coordinates must be listed in order around the boundary of the polygon. We will arrange the points in sequence and then close the loop by repeating the first point at the end.

So the coordinates will be:

$(0, 0), (6, 0), (94, 5), (2, 4), (0, 0)$

Shoelace formula:

The area $A$ of the polygon is given by the formula:

$A = \frac{1}{2} \left| \sum (x_i \cdot y_{i+1} - x_{i+1} \cdot y_i) \right|$

Where $(x_i, y_i)$ are the coordinates of the vertices and the sum runs over all vertices.

Now, let's break it down into steps:

$A = \frac{1}{2} \left| (0 \cdot 0 + 6 \cdot 5 + 94 \cdot 4 + 2 \cdot 0) - (0 \cdot 6 + 0 \cdot 94 + 5 \cdot 2 + 4 \cdot 0) \right|$

Step-by-step calculations:

1. First part (positive terms):

$0 \cdot 0 = 0$ $6 \cdot 5 = 30$ $94 \cdot 4 = 376$ $2 \cdot 0 = 0$

Sum of positive terms = $0 + 30 + 376 + 0 = 406$

2. Second part (negative terms):

$0 \cdot 6 = 0$ $0 \cdot 94 = 0$ $5 \cdot 2 = 10$ $4 \cdot 0 = 0$

Sum of negative terms = $0 + 0 + 10 + 0 = 10$

Now calculate the absolute difference:

$A = \frac{1}{2} \left| 406 - 10 \right| = \frac{1}{2} \times 396 = 198$

Final Answer:

The total area of the garden plot is 198 square feet.

Would you like further clarification or additional details? Here are some related questions:

1. How does the shoelace theorem work in 3D geometry?
2. Can the shoelace theorem be used for non-convex polygons?
3. What other methods can we use to calculate areas of irregular polygons?
4. How do you calculate the area of a garden plot using trigonometry?
5. Can the formula be extended to polygons with more than four vertices?

Tip: Always double-check the order of the points when using the shoelace formula to avoid errors in the final calculation.