To find the area of rectangle ABCD, we need to determine the lengths of two adjacent sides of the rectangle, either the length or the width.
Given the vertices of the rectangle:
- \( A(3, 4) \)
- \( B(-5, 4) \)
- \( C(-5, 8) \)
- \( D(3, 8) \)
From the coordinates, we can see that points A and B have the same y-coordinate (4), so line segment AB is horizontal. Similarly, points C and D have the same y-coordinate (8), indicating that line segment CD is also horizontal.
Now we can find the lengths of AB and AD (or BC and CD, which are the same lengths since it's a rectangle):
-
Length of AB: \[ AB = |x_2 - x_1| = |-5 - 3| = | -8 | = 8 \text{ feet} \]
-
Length of AD: \[ AD = |y_2 - y_1| = |8 - 4| = 4 \text{ feet} \]
Now we calculate the area of rectangle ABCD using the formula: \[ \text{Area} = \text{Length} \times \text{Width} = AB \times AD \] \[ \text{Area} = 8 \text{ feet} \times 4 \text{ feet} = 32 \text{ square feet} \]
Thus, the area of rectangle ABCD is 32 square feet.