1. Module 5 Lesson 5 The Area of Polygons Through Composition and Decomposition.notebook
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Answers Problem Set Lesson 2 #1 & 2

2. Module 5 Lesson 5 The Area of Polygons Through Composition and Decomposition.notebook
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Answers Problem Set Lesson 3 #1 & 3

3. Module 5 Lesson 5 The Area of Polygons Through Composition and Decomposition.notebook
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Answers Problem Set Lesson 3 #1 & 3

4. Module 5 Lesson 5 The Area of Polygons Through Composition and Decomposition.notebook
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Answers Problem Set Lesson 4 #3 & 6

5. Module 5 Lesson 5 The Area of Polygons Through Composition and Decomposition.notebook
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Answers Problem Set Lesson 4 #3 & 6

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MODULE 5 Area, Surface Area, and Volume
Problems
Topic A: Area of Triangles, Quadrilaterals, and
Polygons
Lesson 5: The Area of Polygons Through
Composion and Decomposion

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The base word, compose, is a verb that means the act of
joining or putting together.
Decompose means the opposite, to take apart.
In this lesson, the words composition and decomposition are
used to describe how irregular figures can be separated into
triangles and other polygons. The area of these parts can then
be added together to calculate the area of the whole figure.

8. Module 5 Lesson 5 The Area of Polygons Through Composition and Decomposition.notebook
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9. Module 5 Lesson 5 The Area of Polygons Through Composition and Decomposition.notebook
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Example 1: Decomposing Polygons into Rectangles
The Intermediate School is producing a play that needs a special stage built. A diagram is shown below
(not to scale).
a. On the first diagram, divide the stage into three rectangles using two horizontal
lines. Find the dimensions of these rectangles and calculate the area of each. Then
find the total area of the stage.
Rectangle 1 Rectangle 2 Rectangle 3

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b. On the second diagram, divide the stage into three rectangles using two
vercal lines. Find the dimensions of these rectangles and calculate the area of
each. Then find the total area of the stage.
Rectangle 1 Rectangle 2 Rectangle 3

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c. On the third diagram, divide the stage into three rectangles using one
horizontal line and one vercal line. Find the dimensions of these rectangles and
calculate the area of each. Then find the total area of the stage.
Rectangle 1 Rectangle 2 Rectangle 3

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d. Consider this as a large rectangle with a piece removed.
i. What are the dimensions of the large rectangle and the small rectangle?
ii. What are the areas of the two rectangles?
iii. What operaon is needed to find the area of the original figure?
iv. What is the difference in area between the two rectangles?
v. What do you noce about your answers to (a), (b), (c), and (d)?
vi. Why do you think this is true?

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Example 3: Decomposing Trapezoids
The trapezoid below is a scale drawing of a garden plot.
Find the area of both triangles ABC and ACD.
Then find the area of the trapezoid.
Find the area of both triangles ABD and BCD.
Then find the area of the trapezoid.

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How else can we find this area?

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Closing
Please take out your exit ticket for Lesson 5, close your
binder, and complete the exit ticket. This will be collected.
§ How can we find the area of irregularly shaped polygons?
ú They can be broken into rectangles and triangles; we can then calculate the
area of the figure using the formulas we already know.
§ Which operaons did we use today to find the area of our irregular polygons?
ú Some methods used addion of the area of the parts. Others used
subtracon from a surrounding rectangle.