Rectangle \[ABCD\] is graphed in the coordinate plane. The following are the vertices of the rectangle: \[A(2, 0)\], \[B(6, 0)\], \[C(6, 7)\], and \[D(2, 7)\].

**What is the area of rectangle \[ABCD\]?**

 square units

To find the area of rectangle \( ABCD \), we can use the formula for the area of a rectangle:

\[
\text{Area} = \text{length} \times \text{width}
\]

### Step 1: Identify the vertices
The vertices of the rectangle \( ABCD \) are:
- \( A(2, 0) \)
- \( B(6, 0) \)
- \( C(6, 7) \)
- \( D(2, 7) \)

### Step 2: Calculate the length
The length of the rectangle is the distance between points \( A(2, 0) \) and \( B(6, 0) \). Since these points lie on the x-axis, the length is simply the difference in the x-coordinates:
\[
\text{Length} = |6 - 2| = 4 \text{ units}
\]

### Step 3: Calculate the width
The width of the rectangle is the distance between points \( B(6, 0) \) and \( C(6, 7) \). Since these points lie on the same vertical line, the width is the difference in the y-coordinates:
\[
\text{Width} = |7 - 0| = 7 \text{ units}
\]

### Step 4: Calculate the area
Now, multiply the length by the width to find the area:
\[
\text{Area} = 4 \times 7 = 28 \text{ square units}
\]

### Final Answer:
The area of rectangle \( ABCD \) is \( 28 \) square units.

Would you like further details, or do you have any questions?

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Here are 8 related questions you might find interesting:
1. How do you calculate the perimeter of a rectangle using vertex coordinates?
2. What is the distance formula, and how is it applied in coordinate geometry?
3. How can the slope of the sides of a rectangle be used to confirm right angles?
4. How do you determine the coordinates of the midpoint of a rectangle?
5. Can you find the area of a rectangle using the diagonal length?
6. How can transformations (e.g., translation, rotation) affect the coordinates of a rectangle?
7. How do you prove that a quadrilateral is a rectangle using its vertices?
8. How do you calculate the area of a triangle given its vertices?

**Tip:** When working with rectangles on a coordinate plane, always check if the sides are parallel to the axes to simplify distance calculations!

Learn how to calculate the area of rectangle ABCD with vertex coordinates (2, 0), (6, 0), (6, 7), and (2, 7) using the distance formula and area formula. This problem involves coordinate geometry and is suitable for Grades 6-8.

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