Weaving a Rug
Area and Perimeter of
Rectangles and Squares
Learning Goals
In this lesson, you will:





Calculate the area of rectangles and squares.
Calculate the perimeter of rectangles and squares.
Write a formula for the perimeter and area of a rectangle and a square.
Determine the effect of altering the dimensions of a rectangle or a square on the perimeter and area.
Calculate the area of composite figures.
C
arpets and rugs have been art forms in the Middle East for centuries. Its
history spans before the religions of Islam and Christianity. What is even more
remarkable is that carpet making and rug weaving is still an important part of the economy of many Middle Eastern countries. Many experts have estimated
that rug weaving brought in approximately $420 million dollars to the Iranian
economy in 2008. And rug weaving is quite a popular occupation. It is estimated
that there are 1.2 million rug weavers in Iran. With rugs and carpets still being
made by hand, do you think that carpets and rugs can be made by machine? Do
© 2011 Carnegie Learning
you think machine made Persian carpets and rugs will have the same quality of
handmade rugs?
13.2 Area and Perimeter of Rectangles and Squares • 833
Problem 1 A Rectangular Rug
Tyson is currently creating rectangular-shaped rugs.
1. One rectangular rug is seven feet long and three feet wide. Draw a model of this rug on
the grid shown. Each square on the grid represents a square that is one foot long and
one foot wide.
2. What is the area of this rug? Explain your calculation.
3. What is the perimeter of this rug? Explain your calculation.
834 • Chapter 13 Area
© 2011 Carnegie Learning
Are the
units of measure
the same for area
and perimeter?
4. Six different rectangles are drawn on the grid shown. The letters A through F name
each rectangle.
C
A
B
E
F
D
5. Each square on the grid represents a square that is one foot long and one foot wide.
Complete the table to show the length, width, area, and perimeter of each rectangle.
Rectangle
Length (units)
Width (units)
Perimeter (units)
Area (square units)
A
B
C
D
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E
F
13.2 Area and Perimeter of Rectangles and Squares • 835
6. What is an example of two rectangles having the same area, but different dimensions?
a. What are the perimeters of these rectangles?
b. If the areas are equal, are the perimeters always equal?
7. You can determine the perimeter of a rectangle without drawing it if you know the
rectangle’s length and width. Explain how you can do this. Use the table in Question 5
to help you.
8. Write a formula that you can use to calculate the
perimeter of any rectangle. Use  for the length of
the rectangle, w for the width of the rectangle, and
The opposite
sides of a rectangle
are always the
same length.
P for the perimeter.
length and width. Explain how you can do this. Use the table in Question 5 to help you.
836 • Chapter 13 Area
© 2011 Carnegie Learning
9. You can determine the area of a rectangle without drawing it if you know the rectangle’s
10. Write a formula that you can use to calculate the area of any rectangle. Use  for
the length of the rectangle, w for the width of the rectangle, and A for the area of
the rectangle.
11. Can you determine the area of a rectangle if its perimeter is known?
Explain your reasoning.
12. Can you determine the perimeter of a rectangle if its area is known?
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Explain your reasoning.
13.2 Area and Perimeter of Rectangles and Squares • 837
13. For each rectangle, either the length, width, or area is unknown. First, calculate the
value of the unknown measure. Then, calculate the perimeter.
a.
15 feet
21 feet
b.
Area:
48 square
millimeters
8 millimeters
c.
3.5 inches
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Area: 15.75
square inches
838 • Chapter 13 Area
14. Calculate the perimeter and area of a rectangle that is 11 meters long and
5 meters wide.
a.Double the length and width of the rectangle. Calculate the perimeter of the
new rectangle.
b. What effect does doubling the length and width have on the perimeter?
c.Do you think that doubling the length and width will have the same effect on the
area? Explain your reasoning.
© 2011 Carnegie Learning
15. Calculate the area of the rectangle that had its dimensions doubled.
16. What effect does doubling the length and width have on the area?
13.2 Area and Perimeter of Rectangles and Squares • 839
Problem 2 A Square Rug
Tyson has also received several requests to create square-shaped rugs.
1. One square rug is seven feet long and seven feet wide. Draw a model of this rug on
the grid shown. Each square on the grid represents a square that is one foot long and
one foot wide.
3. What is the perimeter of this rug? Explain your calculation.
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© 2011 Carnegie Learning
2. What is the area of this rug? Explain your calculation.
4. Six different squares are drawn on the grid. The letters A through F name each square.
Each square on the grid represents a square that is one foot long and one foot wide.
C
A
B
E
F
D
5. Complete the table to show the length, width, area, and perimeter of each square.
Square
Length
(units)
Width
(units)
Perimeter
(units)
Area
(square units)
A
B
© 2011 Carnegie Learning
C
D
E
F
13.2 Area and Perimeter of Rectangles and Squares • 841
6. You can determine the perimeter of a square without drawing the square if you know
the length of one side of the square. Explain how you can do this. Use the table in
Question 5 to help you.
7. Write a formula that you can use to calculate the perimeter of any square.
Use s for the side length of the square and P for the perimeter.
8. You can determine the area of a square without drawing it if you know the length of
one side of the square. Explain how you can do this. Use the table in Question 5 to
help you.
9. Write a formula that you can use to calculate the area of any square. Use s for the
length of a side of the square and A for the area of the square.
10. Calculate the value of the unknown side length, area, and perimeter in each square shown.
a.
b.
Area: 169 square feet
842 • Chapter 13 Area
© 2011 Carnegie Learning
5 centimeters
11. Calculate the perimeter and area of a square that has a side length equal to 9 inches.
a.Double the side length of the square. Calculate the perimeter of the new square.
b.What effect does doubling the side length of a
square have on the perimeter?
Is your
reasoning about the
effect of changing side
lengths of a square, the
same or different than
your reasoning when you
considered side length
changes of a rectangle?
c.Do you think that doubling the side length of a
square will have the same effect on the area?
Explain your reasoning.
12. Calculate the area of a square that has a side length equal to
© 2011 Carnegie Learning
10 meters.
a.Double the length of the side of the square. Calculate the area of
the new square.
b.What effect does doubling the length of a side of a square have on the area?
13.2 Area and Perimeter of Rectangles and Squares • 843
Problem 3 A Brand New Floor
A carpeting company has been hired to install flooring on the first floor of a home.
A diagram of this first floor is shown.
35 feet
10 feet
10 feet
5 feet
Enclosed
porch
Dining
room
Kitchen
8 feet
a
Living
room
b
14 feet
10 feet
12 feet
1. Calculate the unknown lengths a and b.
Use what
you do know from
the diagram to
figure out what
you don't know.
2. The homeowners would like to install indoor/outdoor carpeting on the
enclosed porch. How many square feet of indoor/outdoor carpeting
© 2011 Carnegie Learning
will be needed?
844 • Chapter 13 Area
3. The homeowners would like to install wood flooring in the dining room. How many
square feet of wood flooring will be needed?
4. The homeowners would like to install tile in the kitchen. How many square feet of tile
will be needed?
5. The homeowners would like to install loop carpeting in the living room. How many
© 2011 Carnegie Learning
square feet of loop carpeting will be needed?
6. What is the total area of the first floor? Explain your reasoning.
13.2 Area and Perimeter of Rectangles and Squares • 845
7. An employee from the flooring company must now calculate the total cost of the
materials used to complete this job.
a.The carpeting for the porch costs $1.20 per square foot. Calculate the cost of
carpeting the enclosed porch.
b. The loop carpeting costs $0.84 per square foot. Calculate the cost of carpeting
the living room.
c. The wood flooring costs $4.50 per square foot. Calculate the cost of installing the
wood flooring in the dining room.
d. The tiling costs $4.25 per square foot. Calculate the cost of tiling the kitchen.
e. Calculate the total cost of the materials needed for the job.
g. After the homeowners saw the total cost of the flooring for the job, they decided that
the wood flooring was too expensive and decided to use the same loop carpeting in
the dining room as in the living room. Calculate the total cost of the flooring for the first
floor if the homeowners decide to buy the loop carpeting for the dining room.
Be prepared to share your solutions and methods.
846 • Chapter 13 Area
© 2011 Carnegie Learning
f. Do you think the total cost is accurate? Why or why not?