Lesson 13.

3
Name
Area of Combined Rectangles Measurement and Data—
Essential Question How can you find the area of combined rectangles? 4.MD.A.3
MATHEMATICAL PRACTICES
MP1, MP4, MP5

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the Problem
Problem
8m
Jan is visiting a botanical garden with her family.
The diagram shows two rectangular sections of the Rose Garden 3m
garden. What is the total area of the 7m
two sections? Herb
4m
Garden
There are different ways to find the area of
4m
combined rectangles.

One Way Count square units.

Materials ■ grid paper
• Draw the garden on grid paper. Then find the area of
each section by counting squares inside the shape.

Rose Garden Herb Garden

Area = _ square meters Area = _ square meters

• Add the areas.

_ + _ = _ square meters
1 square 5 1 square meter

Another Way Use the area formula for a rectangle.

A Rose Garden B Herb Garden

A= b × h A= b × h

=_×_ =_×_

= _ square meters = _ square meters

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• Add the areas.

_ + _ = _ square meters Math MATHEMATICAL PRACTICES 1

Talk
So, the total area is _ square meters. Analyze Is there another
way you could divide the
figure to find the total
area? Explain.

Chapter 13 729
 Example
Greg is laying carpet in the space outside his laundry room. 8 ft 16 ft
The diagram shows where the carpet will be installed. The
space is made of combined rectangles. What is the area of 17 ft
the carpeted space? 9 ft
24 ft
You can find the area using addition or subtraction.

One Way Use addition.

Rectangle A Rectangle B

A=b×h A=b×h 8 ft 16 ft

=8×_ = _ × 17 B 17 ft
9 ft A
= __ = __
24 ft
Sum of the areas:

__ + __ = __ square feet

Another Way Use subtraction.

Area of whole space Area of missing section

A=b×h A=b×h 16 ft

= 24 × _ =_×_ 17 ft
9 ft 8 ft
= __ = __
24 ft
Difference between the areas:

__ − __ = __ square feet
So, the area of the carpeted space is __ square feet.

• Is there another way you could divide the figure to find the total
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area? Explain.

730
 Name

MATH
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1. Explain how to find the total area of the figure.

Find the area of the combined rectangles.

2. 3. 4.
12 mm 10 mi 2 mi 4 ft 4 ft 4 ft
3 mm 8 mi
9 mm 8 ft
6 mm 9 mi 8 ft 8 ft
7 mi
6 mm 16 ft
18 mi

Math MATHEMATICAL PRACTICES 6

Talk
Describe the characteristics
On of combined rectangles.
On Your
Your Own
Own
Find the area of the combined rectangles. 6 yd
MATHEMATICAL
5. PRACTICE 6
Attend to Precision Jamie’s mom wants to
12 yd
enlarge her rectangular garden by adding a new rectangular
New
section. The garden is now 96 square yards. What will the Section
14 yd
total area of the garden be after she adds the new section? 8 yd

6. DEEPERExplain how to find the perimeter and area 4 ft

of the combined rectangles at the right.
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9 ft

12 ft

Chapter 13 • Lesson 3 731

 MATHEMATICAL PRACTICES COMMUNICA5&
t
1&34E7&3&
t
CONSTRUCT ARGUMENTS

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the Problem
Problem

7. SMARTER
The diagram shows the layout of
Mandy’s garden. The garden is the shape of combined
rectangles. What is the area of the garden?
a. What do you need to find?–

b. How can you divide the figure to help you find  
 
the total area? – 1 ft

7 ft 1 ft 3 ft
c. What operations will you use to find the answer? 5 ft
3 ft

d. Draw a diagram to show how you divided the figure.

Then show the steps to solve the problem.

WRITE M
t Show Your Work

Math

So, the area of the garden is ___ .

Personal Math Trainer

8. SMARTER Workers are painting a large letter L for an outdoor 2 ft
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sign. The diagram shows the dimensions of the L. For numbers 8a–8c,
select Yes or No to tell whether you can add the products to find the
area that the workers will paint.
8 ft
8a. 2 × 8 and 2 × 4 Yes No

8b. 2 × 6 and 2 × 8 Yes No

8c. 2 × 6 and 6 × 2 Yes No 2 ft

6 ft

732
 Practice and Homework
Name
Lesson 13.3
Area of Combined Rectangles
COMMON CORE STANDARD—4.MD.A.3
Solve problems involving measurement and
conversion of measurements from a larger unit
Find the area of the combined rectangles. to a smaller unit.
1. 2m 2. 9 ft 3. 9 in.
5 ft
5 in.
A 6m
5 ft
10 m 5m 11 in.
12 ft
B 4m 7 ft 6 in.

7m
3 in.
14 ft

Area A = 2 × 6,
Area B = 7 × 4
12 + 28 = 40

40 square meters

Problem
Problem Solving
Solving
Use the diagram for 4–5. 4. What is the area of the space that Nadia has
Nadia makes the diagram below to represent shown for scrapbooking?
the counter space she wants to build in her
craft room.
3 ft ______

11 ft 5 ft 5. What is the area of the space she has shown

15 ft for painting?
Painting
9 ft
Scrapbooking

13 ft
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______

6. WRITE Math Write a word problem that involves

combined rectangles. Include a diagram and the solution.

Chapter 13 733
Lesson Check (4.MD.A.3)
1. What is the area of the combined rectangles 2. Marquis is redecorating his bedroom. What
below? could Marquis use the area formula to find?
20 yd

3 yd
5 yd
12 yd

Spiral Review (4.OA.B.4, 4.MD.A.1, 4.MD.A.3)

3. Giraffes are the tallest land animals. A male 4. Drew purchased 3 books each with a
giraffe can grow as tall as 6 yards. How tall different price, for $24. The cost of each book
would the giraffe be in feet? was a multiple of 4. What could be the prices
of the 3 books?

5. Esmeralda has a magnet in the shape 6. What is the area of the rectangle below?
of a square. Each side of the magnet is
3 inches long. What is the perimeter of
9 feet
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her magnet?

7 feet

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