To find the area of rectangle ABCD, we can use the coordinates of its vertices:
- A(0, -1)
- B(0, 4)
- C(4, 4)
- D(4, -1)
First, we need to determine the lengths of the sides of the rectangle.
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Length of AB and CD (vertical sides):
- The y-coordinates of points A and B are \(y_A = -1\) and \(y_B = 4\).
- The length of AB (or CD) is calculated as:
\[ |y_B - y_A| = |4 - (-1)| = |4 + 1| = 5 \text{ units} \]
-
Length of BC and AD (horizontal sides):
- The x-coordinates of points B and C are \(x_B = 0\) and \(x_C = 4\).
- The length of BC (or AD) is calculated as:
\[ |x_C - x_B| = |4 - 0| = 4 \text{ units} \]
Now we can calculate the area of the rectangle using the formula: \[ \text{Area} = \text{Length} \times \text{Width} \] Substituting the lengths we found: \[ \text{Area} = 5 \times 4 = 20 \text{ square units} \]
Therefore, the area of rectangle ABCD is 20 square units.
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