Basic Mathematics for College Students

In everyday life, we often use areas. For example,

• To carpet a room, we buy square yards.


• A can of paint will cover a certain number of square feet.


• To measure vast amounts of land, we often use square miles.


• We buy house roofing by the “square.” One square is 100 square feet.
  The rectangle shown below has a length of 10 centimeters and a width of
  3 centimeters. If we divide the rectangular region into square regions as shown in the
  figure, each square has an area of 1 square centimeter—a surface enclosed by a square
  measuring 1 centimeter on each side. Because there are 3 rows with 10 squares in each
  row, there are 30 squares. Since the rectangle encloses a surface area of 30 squares, its
  area is 30 square centimeters, which can be written as 30 cm^2.
  This example illustrates that to find the area of a rectangle, we multiply its length
  by its width.

780 Chapter 9 An Introduction to Geometry

One square inch

(1 in.^2 )

One square centimeter

(1 cm^2 )

1 in. 1 in. 1 cm 1 cm

1 cm

1 cm

1 in.

1 in.

1 cm^2

10 cm

3 cm

Caution! Do not confuse the concepts of perimeter and area. Perimeter is

the distance around a polygon. It is measured in linear units, such as

centimeters, feet, or miles. Area is a measure of the surface enclosed within a

polygon. It is measured in square units, such as square centimeters, square feet,

or square miles.

In practice, we do not find areas of polygons by counting squares. Instead, we use

formulas to find areas of geometric figures.

2 Find the area of a polygon.

The areaof a polygon is the measure of the amount of surface it encloses. Area

is measured in square units, such as square inches or square centimeters, as shown

below.