To find the area of rectangle ABCD given the coordinates of its vertices, we can follow these steps:
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Identify the coordinates:
- A: (3, 4)
- B: (-5, 4)
- C: (-5, 8)
- D: (3, 8)
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Calculate the lengths of the sides of the rectangle:
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The length of side AB (or CD) can be calculated by finding the distance between points A and B: \[ \text{Length} = |x_A - x_B| = |3 - (-5)| = |3 + 5| = 8 \text{ units} \]
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The length of side BC (or AD) can be calculated by finding the distance between points B and C: \[ \text{Width} = |y_C - y_B| = |8 - 4| = 4 \text{ units} \]
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Calculate the area of the rectangle: \[ \text{Area} = \text{Length} \times \text{Width} = 8 \text{ units} \times 4 \text{ units} = 32 \text{ square units} \]
Given your answer choices, the correct answer for the area of rectangle ABCD is: 32 square feet.