Question

a rectangle is shown on a coordinate plane with points ABCD
A: 3, 4
B: -5, 4
C: -5, 8
D: 3, 8
Find the area of rectangle ABCD in square feet
32 feet
32 square feet
-32 square feet
24 feet

Answer 1

To find the area of rectangle ABCD given the coordinates of its vertices, we can follow these steps:

1. **Identify the coordinates:**
- A: (3, 4)
- B: (-5, 4)
- C: (-5, 8)
- D: (3, 8)

2. **Calculate the lengths of the sides of the rectangle:**
- The length of side AB (or CD) can be calculated by finding the distance between points A and B:
\[
\text{Length} = |x_A - x_B| = |3 - (-5)| = |3 + 5| = 8 \text{ units}
\]

- The length of side BC (or AD) can be calculated by finding the distance between points B and C:
\[
\text{Width} = |y_C - y_B| = |8 - 4| = 4 \text{ units}
\]

3. **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.**