To find the area of rectangle ABCD, we need to determine the lengths of its sides. Using the coordinates of the vertices, we can find these lengths.
**Coordinates of the vertices:**
- Point \( A = (3, 4) \)
- Point \( B = (-5, 4) \)
- Point \( C = (-5, 8) \)
- Point \( D = (3, 8) \)
First, identify the length of one pair of opposite sides (horizontal sides, AB and CD):
- The length from \( A \) to \( B \): \( \left|3 - (-5)\right| = \left|3 + 5\right| = 8 \)
Next, identify the length of the other pair of opposite sides (vertical sides, AD and BC):
- The length from \( A \) to \( D \): \( \left|4 - 8\right| = \left|4 - 8\right| = 4 \)
Now, calculate the area of the rectangle using the formula for the area of a rectangle:
\[ \text{Area} = \text{length} \times \text{width} = 8 \times 4 = 32 \]
Therefore, the area of rectangle \( ABCD \) is \( 32 \) square units.
Use the image to answer the question.
A coordinate plane shows the x-axis ranging from negative 9 to 9 in unit increments and the y-axis ranging from negative 11 to 11 in unit increments. Four plotted points upper A upper B upper C upper D are joined to form a rectangle. The coordinates of the plotted points are as follows: point upper A is left parenthesis 3 comma 4 right parenthesis, point upper B is left parenthesis negative 5 comma 4 right parenthesis, point upper C is left parenthesis negative 5 comma 8 right parenthesis, and point upper D is left parenthesis 3 comma 8 right parenthesis.
Find the area of rectangle ABCD in square feet.
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