MA005: Calculus I

One reason "areas" are so useful is that they can represent quantities other than simple geometric shapes. For example, if the units of the base of a rectangle are "hours" and the units of the height are "miles/hour", then the units of the "area" of the rectangle are ("hours").("miles/hour") = "miles," a measure of distance (Fig. 13a). Similarly, if the base units are "centimeters" and the height units are "grams" (Fig. 13b), then the "area" units are "gram.centimeters," a measure of work.