Consider the rectangle in the coordinate plane enclosed by the vertical lines x = -4 and x = 2 and the horizontal lines y = -2 and y = 3. What is the area of this rectangle in square units?

Introduction / Context:
This problem is about finding the area of an axis-aligned rectangle in the coordinate plane. The sides of the rectangle are given as lines of constant x and constant y values. Such questions test your understanding of distance on the number line and how it translates into side lengths for rectangles.

Given Data / Assumptions:

• Vertical boundaries are x = -4 and x = 2.
• Horizontal boundaries are y = -2 and y = 3.
• The region enclosed by these lines is a rectangle.
• We need the area in square units.

Concept / Approach:
For a rectangle aligned with the axes, its side lengths are simply the differences between the respective x-coordinates and y-coordinates: Width = right x - left x Height = top y - bottom y Then area A is: A = width * height

Step-by-Step Solution:
Left x-coordinate = -4, right x-coordinate = 2. Width = 2 - (-4) = 2 + 4 = 6 units. Bottom y-coordinate = -2, top y-coordinate = 3. Height = 3 - (-2) = 3 + 2 = 5 units. Now compute area: A = width * height = 6 * 5. Therefore, A = 30 square units.

Verification / Alternative check:
We can visualise or quickly sketch the rectangle with corners at (-4, -2), (2, -2), (2, 3), and (-4, 3). Counting squares on a grid would show 6 units across and 5 units up, confirming our multiplication and resulting area of 30.

Why Other Options Are Wrong:
20 and 25 result from using one correct side (e.g., 5 or 6) but pairing it with an incorrect second side (4 or 5). 40 would come from mistakenly taking one of the side lengths as 8 or misreading coordinates. None of these respect both x and y ranges simultaneously.

Common Pitfalls:
People sometimes subtract in the wrong order or forget that subtracting a negative adds. Another common oversight is to mix up horizontal and vertical differences. Always compute width from x-values and height from y-values separately.

Final Answer:
The area of the enclosed rectangle is 30 square units.