Question

Find the area of rectangle ABCD that has vertices point A (-2,4), point B (3,4), point C (-2,-2), and point D (3,-2) in square miles.
30 square miles
1l square miles
35 square miles
25 square miles

Answer 1

To find the area of rectangle ABCD, we need the lengths of its sides. We can calculate the lengths of the sides based on the coordinates of the vertices.

The vertices are:
- A (-2, 4)
- B (3, 4)
- C (-2, -2)
- D (3, -2)

1. **Calculate the length of side AB**:
- The y-coordinates of points A and B are the same, which is 4.
- The length of AB can be calculated as the difference in x-coordinates:
\[
AB = x_B - x_A = 3 - (-2) = 3 + 2 = 5
\]

2. **Calculate the length of side AD**:
- The x-coordinates of points A and D are the same, which is -2.
- The length of AD can be calculated as the difference in y-coordinates:
\[
AD = y_A - y_D = 4 - (-2) = 4 + 2 = 6
\]

3. **Calculate the area of rectangle ABCD**:
- The area \(A\) of a rectangle is given by the formula:
\[
A = \text{length} \times \text{width}
\]
- Plugging in the lengths we found:
\[
A = AB \times AD = 5 \times 6 = 30
\]

Thus, the area of rectangle ABCD is **30 square miles**.