To calculate the area of the rectangle shown:

Step 1: Determine the length and width

The coordinates of the rectangle's vertices are:

• Top-left: $(3, 7)$
• Top-right: $(8, 7)$
• Bottom-left: $(3, 4)$
• Bottom-right: $(8, 4)$

1. Length: The horizontal distance between the points $(3, 7)$ and $(8, 7)$ is: $|8 - 3| = 5$

2. Width: The vertical distance between the points $(3, 7)$ and $(3, 4)$ is: $|7 - 4| = 3$

Step 2: Calculate the area

The area of a rectangle is given by: $\text{Area} = \text{Length} \times \text{Width}$ Substituting the values: $\text{Area} = 5 \times 3 = 15$

Final Answer:

The area of the rectangle is 15 square units.

Would you like further clarification or details?

Here are 5 related questions to explore:

1. How do you find the perimeter of this rectangle?
2. What happens to the area if the length is doubled?
3. Can you determine the area of a triangle formed by three of these points?
4. What formula applies if the rectangle is rotated on a plane?
5. How would the area calculation change if it were a parallelogram instead?

Tip: Always confirm your measurements by carefully observing coordinate differences in both dimensions.