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Teacher Copy
Lesson 23-2
Perimeter and Area of Composite Figures
Learning Targets
Model the area of a parallelogram by decomposing into triangles.
Find the area of a special quadrilateral by decomposing into triangles.
Write equations that represent problems related to the area of parallelograms and
rectangles.
Solve problems involving the area of parallelograms and rectangles.
Find the area of special quadrilaterals and polygons by composing into rectangles or
decomposing into triangles and other shapes.
Identify a Subtask (Learning Strategy)
Definition
Breaking a problem into smaller pieces whose outcomes lead to a solution
Purpose
Helps to organize the pieces of a complex problem and reach a complete solution
Use Manipulatives (Learning Strategy)
Definition
Using objects to examine relationships between the information given
Purpose
Provides a visual representation of data that supports comprehension of information in a problem
Create Representations (Learning Strategy)
Definition
Creating pictures, tables, graphs, lists, equations, models, and /or verbal expressions to interpret
text or data
Purpose
Helps organize information using multiple ways to present data and to answer a question or show
a problem solution
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Think-Pair-Share (Learning Strategy)
Definition
Thinking through a problem alone, pairing with a partner to share ideas, and concluding by
sharing results with the class
Purpose
Enables the development of initial ideas that are then tested with a partner in preparation for
revising ideas and sharing them with a larger group
Discussion Groups (Learning Strategy)
Definition
Working within groups to discuss content, to create problem solutions, and to explain and justify
a solution
Purpose
Aids understanding through the sharing of ideas, interpretation of concepts, and analysis of
problem scenarios
Sharing and Responding (Learning Strategy)
Definition
Communicating with another person or a small group of peers who respond to a piece of writing
or proposed problem solution
Purpose
Gives students the opportunity to discuss their work with peers, to make suggestions for
improvement to the work of others, and/or to receive appropriate and relevant feedback on their
own work
Interactive Word Wall (Learning Strategy)
Definition
Visually displaying vocabulary words to serve as a classroom reference of words and groups of
words as they are introduced, used, and mastered over the course of a year
Purpose
Provides a visual reference for new concepts, aids understanding for reading and writing, and
builds word knowledge and awareness
Suggested Learning Strategies
Identify a Subtask, Use Manipulatives, Create Representations, Think-Pair-Share, Discussion
Groups, Sharing and Responding, Interactive Word Wall
Pictured is an aerial view of one of the possible playground designs. An aerial view is the p. 295p. 294
view from above something.
1. Look at the shape of each figure. What piece of playground equipment do you think each
figure represents?
2. List all the geometric shapes you can identify in each figure in the playground to
complete the table.
Figure
Geometric
Shape(s)
A
B
C
D
E
F
3. The diagram shows the dimensions of Figure E.
What is the perimeter of Figure E? Explain how you found the perimeter.
4. What is the area of Figure E? Explain how you found the area. Then write a rule or
equation that could be used to find the area of any rectangle.
5. There is also a parallelogram in the playground design. List some characteristics of a
parallelogram.
6. Use appropriate tools strategically.
a. Cut out the parallelogram on page 303. Then cut a right triangle from one side of the
parallelogram so that you can form a rectangle with the two pieces. Put the two pieces
together to form a rectangle.
b. Use a ruler to measure the rectangle you cut out and find its area.
c. How do the lengths of the base and the height of the rectangle formed from the
parallelogram relate to those of the original parallelogram?
7. What is the relationship between the area of a parallelogram and its base and height?
Describe the relationship using words, symbols, or both. Write a rule or equation for
finding the area of any parallelogram.
Math Terms
Perimeter is the distance around a figure.
Perimeter is measured in linear units, for example, feet or ft.
Area is the number of square units a figure covers.
Area is measured in square units, for example, square feet or ft2.
The area, A, of a rectangle or a parallelogram is equal to the length of the base, b, times the
height, h: A = b × h.
Academic Vocabulary
Composite means made up of various separate parts or pieces.
8. The diagram shows the dimensions of Figure B, the ball pit in the playground. What is the
area of Figure B?
A composite figure is a figure that can be decomposed into two or more figures. You can
find the area of a figure that can be decomposed, or divided, into rectangles and
parallelograms.
9. Persevere in problem solving. The diagram shows the shape of a playground in a park.
a. Fill in missing dimensions on the playground. Then find the perimeter of the
playground.
b. The playground can be decomposed into a parallelogram and two rectangles. Use a
colored pencil to draw lines on the diagram to decompose the figure. Explain how to
use the shapes you just drew to find the area of the playground.
c. Use the rules or equations you wrote in Items 4 and 7 to find the area of the
playground. Justify your answer.
Check Your Understanding
For Items 10 and 11, find the perimeter and area of each figure.
10.
11.
12. Draw the rectangle that would result from rearranging the parallelogram in Item 11. How
does the area of this rectangle compare to the area of the parallelogram in Item 11?
13. The area of a rectangle is 100 square feet. If the width is 25 feet, explain how to find the
length of the base.
Lesson 23-2 Practice
For Items 14–17, find each perimeter and use the rules or equations you wrote in Items 4
and 7 to find the area of each figure.
14.
15.
16.
17.
18. Reason quantitatively. A square tablecloth has a perimeter of 12 feet. What is the area of
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the tablecloth?
19. A square field has an area 121 square meters. What is the perimeter of the field?
20. The area of a parallelogram with a height of 6 meters is 126 square meters. What is the
base length of the parallelogram?
21. A rectangular pool is 9 feet wide. The pool has an area of 117 square feet. What is the
perimeter of the pool?
22. A rectangular floor is 12 feet wide and 18 feet long. How much will it cost to carpet the
floor if the carpet costs $1.39 per square foot?
23. Make sense of problems. Jamie has to put 2 coats of paint on 6 rectangular walls. Each
wall is 9 feet by 15 feet. Each can of paint covers 500 square feet. How many cans of paint
should Jamie buy? Explain your thinking.
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