Final answer:
The area of a rectangle with length l and width w is given by the expression lw. To compare areas, ratios and proportions can be used, assuming the dimensions are known. Changes in cross-sectional area are proportional to the original area.
Step-by-step explanation:
For a rectangle with length l and width w, the area is calculated by multiplying the length by the width, which is lw. Therefore, the correct expression for the area of rectangle ABCD is lw. Regarding the comparison of areas of ABCD and A'B'C'D', if the dimensions of ABCD are given by l and w and no additional information is provided about A'B'C'D', it is not possible to directly compare their areas without further details.
When comparing the change in cross-sectional area for two different blocks as a function of a change in their dimensions, it is important to remember that the change in area is proportional to the area itself. For example, if Block A has a cross-sectional area of 2L² and Block B has an area of 4L², then any change in the cross-sectional area of Block B would be twice that of Block A because its area is twice as large.
To compare the areas of two different shapes or objects, we often use ratios or proportions. This enables us to understand the relationship between the two areas quantitatively. Calculating or comparing the areas requires knowledge of their dimensions, such as length and width for rectangles, and the use of appropriate formulas for each shape.