Final answer:
The total area under a polygon does not necessarily equal the total area under a histogram as they represent different types of data and are used for different purposes in mathematics and statistics. The correct option is B.
Step-by-step explanation:
The total area under a polygon does not necessarily equal the total area under a histogram, as the two are used to represent different types of data and information visually.
A polygon, in mathematical terms, can be any closed plane figure with at least three straight sides and angles, and the area under it is simply the space contained within those sides. A histogram, however, is used specifically in statistics to represent the frequency distribution of quantitative data; it consists of adjacent bars whose heights correspond to frequency values.
The total area under the histogram represents the cumulative frequency of the data, and unless by coincidence, this area is not related to the area under a geometric polygon.
To further illustrate: if you have a histogram showing the distribution of ages among a group of people, the total area under the histogram is important for probability calculations, as it correlates to the dataset itself, whereas the shape and area of a polygon have no direct correlation with the histogram's data or the frequency of occurrences.