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Chapter 9: Problem 77

Describe how area is measured. Explain why linear units cannot be used.

Short Answer

Expert verified
Area, a two-dimensional concept encompassing both length and width, is measured in square units. Linear units are insufficient as they only measure one-dimensional concepts such as length.

Step by step solution

01

Understanding Area

Area refers to the amount of space within the boundary of a 2-dimensional shape. It is measured in square units and tells you how much space there is inside the boundary of the shape.
02

Measuring Area

To measure the area of a shape, you need to use square units. The unit of measurement depends on the nature of the shape. For instance, the area of a rectangle is derived by multiplying its length by its width, giving an area in square units. Similarly, the area of a circle is given by \(\pi\) times the square of the radius (\(r^{2}\)), resulting in square units.
03

Why Linear Units Cannot Be Used

Linear units are used to measure the length or distance, which is one-dimensional. When we talk about area, we are referring to a 2-dimensional concept which includes both length and width. A square unit, therefore, is a unit of area that is equal to a square that is one unit on each side. Hence, using linear units alone to measure an area would be inadequate as it wouldn't fully encompass the concept of space within the boundaries of a shape.

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