Final answer:
The area of a rectangle is expressed as the product of its length and width (A = l × w). Dimensional consistency must be maintained in formulas, and units of measurement must be consistent.
Step-by-step explanation:
The expression which correctly shows the area of the rectangle is calculated by multiplying its length and width. In mathematical terms, if the length is represented by l and the width by w, then the area A of the rectangle is A = l × w. It is important to ensure that the units of measurement are consistent when calculating area. For example, if the length and width are given in meters, the resulting area will be in square meters (m²).
When comparing formulas for the area of different shapes, dimensional consistency is key. Formulas like 2lw (which would represent perimeter rather than area) and 2πr (the circumference of a circle) are not dimensionally consistent with the area. Instead, expressions such as l² or w² for squares, and πr² for circles, are dimensionally consistent for representing areas.