Basic Mathematics for College Students

The rectangle in the figure below has a length of 5 centimeters and a width of
3 centimeters. Since each small square region covers an area of one square centimeter,
each small square region measures 1 cm^2. The small square regions form a rectangular
pattern, with 3 rows of 5 squares.

Because there are , or 15, small square regions, the area of the rectangle is
15 cm^2 .This suggests that the area of any rectangle is the product of its length and its width.

length width
By using the letter Ato represent the area of the rectangle, the letter lto represent
the length of the rectangle, and the letter wto represent its width, we can write this
formulain simpler form. Letters (or symbols), such as A, l,and w,that are used to
represent numbers are called variables.

Area of a rectangle 

5  3

3 centimeters

(cm)

5 cm

One square centimeter

(1 cm^2 )

1.4 Multiplying Whole Numbers 49

Area of a Rectangle

The area,A, of a rectangle is the product of the rectangle’s length,l, and its

width,w.

Area lengthwidth or

The formula can be written more simply without the raised dot as Alw.

Alw

EXAMPLE (^11) Gift Wrapping When completely unrolled, a long sheet
of gift wrapping paper has the dimensions shown below. How many square feet of
gift wrap are on the roll?
Strategy We will substitute 12 for the length and 3 for the width in the formula
for the area of a rectangle.
WHY To find the number of square feet of paper, we need to find the area of the
rectangle shown in the figure.
Solution
We translate the words of the problem to numbers and symbols.
is equal to times

=12 3

=36

There are 36 square feet of wrapping paper on the roll. This can be written in more
compact form as 36 ft^2.



The area of

the gift wrap

the width of

the roll.

the length of

the roll

The area of

the gift wrap

3 ft

12 ft

Self Check 11

ADVERTISINGThe rectangular

posters used on small billboards

in the New York subway are 59

inches wide by 45 inches tall.

Find the area of a subway

poster.

Now TryProblems 53 and 55