To find the area of rectangle ABCD, we first need to determine the lengths of its sides. The vertices are given as follows:
- Point A: (2, -5)
- Point B: (5, -5)
- Point C: (5, -1)
- Point D: (2, -1)
Step 1: Find the lengths of the sides.
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The length of side AB (horizontal side) can be calculated as follows: \[ \text{Length of AB} = x_B - x_A = 5 - 2 = 3 \]
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The length of side AD (vertical side) can be calculated as follows: \[ \text{Length of AD} = y_D - y_A = -1 - (-5) = -1 + 5 = 4 \]
Step 2: Calculate the area of the rectangle.
The area of a rectangle is given by the formula: \[ \text{Area} = \text{length} \times \text{width} \] Using the lengths we calculated: \[ \text{Area} = \text{Length of AB} \times \text{Length of AD} = 3 \times 4 = 12 \]
Conclusion:
The area of rectangle ABCD is \( \boxed{12} \) square miles.