Question

What is the area of rectangle ABCD?

coordinate plane with rectangle ABCD at A 0 comma negative 1, B 0 comma 4, C 4 comma 4, and D 4 comma negative 1

16 square units
18 square units
20 square units
25 square units

Answer 1

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.

1. **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:
\[
|y_B - y_A| = |4 - (-1)| = |4 + 1| = 5 \text{ units}
\]

2. **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**.