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!