why area is called a derived quantity
Answers
Answer:
Derived quantities are quantities that are calculated from two or more measurements. They include area, volume, and density. The area of a rectangular surface is calculated as its length multiplied by its width. The volume of a rectangular solid is calculated as the product of its length, width, and height.
Explanation:
In any system of measurement, there are base units and derived units. The base units are the ones that are defined independently, and the derived units are then defined in terms of the base units. Defining base units precisely is a surprisingly difficult problem (you can read about this elsewhere), and you don’t want them to contradict each other, so you want as few base units as possible. Defining derived units is easy; just use the base units you already have.
In the SI system of measurement, there are seven base units. Two of them are the meter for distance and the second for time. From just these two units, you can derive units for velocity (meters/second), acceleration (meters/second^2), area (meters^2), volume (meters^3), and even less standard ones like rate of change of area (meters^2/second). Lots of bang for your buck. It happens that one of the units you can derive measures area.
I could make up some other system with alternative base units. Suppose that in my new system of measurement, the acre is a base unit which measures area. In this system, the unit for area is not a derived unit. Instead, the unit for distance becomes a derived unit, and such a unit for distance would be the square root of an acre (which is about 208.7 feet). There is no logical reason we can’t do this. Every system of measurement I know of has a distance as a base unit and area as a derived unit, presumably because squaring is much easier than square rooting.