# Metric Measurement

## Measuring Area


### Learning Objectives

After completing this section, you should be able to:
1. Identify reasonable values for area applications.
2. Convert units of measures of area.
3. Solve application problems involving area.
Area is the size of a surface. It could be a piece of land, a rug, a wall, or any other two-dimensional surface with attributes that can be measured in the metric unit for distance-meters. Determining the area of a surface is important to many everyday activities. For example, when purchasing paint, you’ll need to know how many square units of surface area need to be painted to determine how much paint to buy.
Square units indicate that two measures in the same units have been multiplied together. For example, to find the area of a rectangle, multiply the length units and the width units to determine the area in square units.
Note that to accurately calculate area, each of the measures being multiplied must be of the same units. For example, to find an area in square centimeters, both length measures (length and width) must be in centimeters.

### Reasonable Values for Area

Because area is determined by multiplying two lengths, the magnitude of difference between different square units is exponential. In other words, while a meter is 100 times greater in length than a centimeter, a square meter  is  times greater in area than a square centimeter . The relationships between benchmark metric area units are shown in the following table.
An essential understanding of metric area is to identify reasonable values for area. When testing for reasonableness you should assess both the unit and the unit value. Only by examining both can you determine whether the given area is reasonable for the situation.

### Converting Units of Measures for Area

Just like converting units of measure for distance, you can convert units of measure for area. However, the conversion factor, or the number used to multiply or divide to convert from one area unit to another, is not the same as the conversion factor for metric distance units. Recall that the conversion factor for area is exponentially relative to the conversion factor for distance. The most frequently used conversion factors are shown in .

### Solving Application Problems Involving Area

While it may seem that solving area problems is as simple as multiplying two numbers, often determining area requires more complex calculations. For example, when measuring the area of surfaces, you may need to account for portions of the surface that are not relevant to your calculation.
When calculating area, you must ensure that both distance measurements are expressed in terms of the same distance units. Sometimes you must convert one measurement before using the area formula.
When calculating area, you may need to use multiple steps, such as converting units and subtracting areas that are not relevant.

### Check Your Understanding


### Key Terms

1. area
2. square units

### Key Concepts

1. Area describes the size of a two-dimensional surface. It is the amount of space contained within the lines of a two-dimensional space.
2. Area is measured in square meters units; in the metric system the base unit for area is square meters ().

### Videos

1. Converting Metric Units of Area
2. Why the Metric System Matters

### Formulas

To determine the area of rectangular-shaped objects:

You can convert between metric area units using the conversion factors shown in .