To calculate the areas of the fields based on the given coordinates, we will need to determine the shapes formed by the points and then use the appropriate formulas to compute the area.
Field A
The points for Field A are:
- (0, 0)
- (4, 7)
- (0, 4)
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Plot the points: The points create a triangle.
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Area of triangle formula: The area \( A \) can be calculated using the formula for the area of a triangle given by vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\): \[ A = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]
Using the points (0, 0), (4, 7), and (0, 4): \[ A = \frac{1}{2} \left| 0(7 - 4) + 4(4 - 0) + 0(0 - 7) \right| \] \[ = \frac{1}{2} \left| 0 + 16 + 0 \right| = \frac{1}{2} \cdot 16 = 8 \text{ square units} \]
Field B
The points for Field B are:
- (0, 0)
- (-4, 0)
- (3, 0)
- (0, -3)
- (3, -3)
This doesn't clearly form a simple shape like a triangle, but we note that it creates:
- A rectangle with height 3 units and width 7 units from (-4, 0) to (3, 0) and height down to (-3).
The area can be computed as: \[ \text{Length} = 7 \quad \text{Height} = 3 \quad \text{Area} = Length \times Height = 7 \times 3 = 21 \text{ square units} \]
Field C
The points for Field C are:
- (7, 3)
- (0, 4)
- (-4, 4)
These points also form a triangle. Using the triangle area formula again:
- Using points (7, 3), (0, 4), and (-4, 4): \[ A = \frac{1}{2} \left| 7(4 - 4) + 0(4 - 3) + -4(3 - 4) \right| \] \[ = \frac{1}{2} \left| 0 + 0 + 4 \right| = \frac{1}{2} \cdot 4 = 2 \text{ square units} \]
Summary of Areas
- Field A: 8 square units
- Field B: 21 square units
- Field C: 2 square units
Now if required, these areas can be converted to acres or square yards based on the conversion factor provided.
1 acre = 4840 sq yards. The areas in square yards can be derived from square units if necessary.
Please clarify if you need specific conversions or additional calculations!