Area and Perimeter of Composite Figures
Putting Back the Pieces
ACTIVITY
5.4
SUGGESTED LEARNING STRATEGIES: Use Manipulatives
According to Chinese legend, a man dropped a porcelain tile. It
broke into the seven pieces you see below. They are called tangram
pieces. While he was trying to reassemble the seven pieces into a
square, he found that he could make hundreds of different shapes.
© 2010 College Board. All rights reserved.
1. Cut out the seven pieces or use a tangram set. Assemble them
into the original square tile.
Unit 5 • Geometry
263
© 2010 College Board. All rights reserved.
This page is blank.
264
Springboard® Mathematics with Meaning™ Level 1
Area and Perimeter of Composite Figures
ACTIVITY 5.4
continued
Putting Back the Pieces
SUGGESTED LEARNING STRATEGIES: Quickwrite, Group
Presentation, Think/Pair/Share, Look for a Pattern
My Notes
2. Use a ruler to measure the square you made from the seven
tangram pieces.
a. What is the area of the square? Use the My Notes space to
show your calculations.
b. What is the perimeter of the square? Show your calculations.
3. At right is another shape that can
be created using all seven tangram
pieces. The shape is not drawn
to scale.
© 2010 College Board. All rights reserved.
a. Reassemble your pieces into
this shape, or create a shape
of your own.
b. What is the area of the shape you just created? Compare the
area to the area you found for the square in Question 2.
c. What is the perimeter of the shape you just created?
Compare the perimeter to the perimeter you found for the
square in Question 2.
4. What can be said about the areas and perimeters of different
shapes that can be formed using all seven tangram pieces?
Unit 5 • Geometry
265
ACTIVITY 5.4
Area and Perimeter of Composite Figures
continued
Putting Back the Pieces
SUGGESTED LEARNING STRATEGIES: Identify a Subtask,
Create Representations, Group Presentation
My Notes
5. Divide the composite figure below into shapes whose area you
know how to find. Use the grid lines as a guide.
a. Determine the area of each shape you made. Show your
work.
CONNECT TO AP
In AP Calculus, an important
problem is finding the area under
a curve. You can count squares on
a coordinate plane to do this.
y 5
4
3
b. Give the total area of the composite figure.
2
1
2
3
4
5
x
You will also learn other procedures
that result in much more precise or
even exact calculations of the area
of irregular figures when you take
calculus.
266
6. Compare and contrast your solution with your classmates.
Springboard® Mathematics with Meaning™ Level 1
© 2010 College Board. All rights reserved.
1
Area and Perimeter of Composite Figures
ACTIVITY 5.4
continued
Putting Back the Pieces
SUGGESTED LEARNING STRATEGIES: Marking the Text,
Quickwrite, Use Manipulatives
My Notes
Tyrone loves to go fishing with his mother. They often fish at Big
Trout Pond in a nearby state park. One day after Tyrone caught
several fish, he was concerned that the pond would run out of
fish. His mother explained that the park rangers routinely restock
the pond.
Tyrone wanted to know how the rangers know how many fish
to add to the pond. Tyrone did some research and learned that the
number of fish that a pond can support depends in part on the
surface area of the pond.
7. Look at the scale drawing of the pond below.
a. Are you able to divide the figure into shapes whose area you
know how to find? Explain why or why not.
b. Carefully cut out the scale drawing of the pond. Then trace it
on the grid on page 269.
© 2010 College Board. All rights reserved.
Big Trout Pond
Unit 5 • Geometry
267
© 2010 College Board. All rights reserved.
This page is blank.
268
Springboard® Mathematics with Meaning™ Level 1
Area and Perimeter of Composite Figures
ACTIVITY 5.4
continued
Putting Back the Pieces
SUGGESTED LEARNING STRATEGIES: Quickwrite, Simplify the
Problem, Think/Pair/Share, Debriefing, Group Presentation
My Notes
c. Shade every square that is completely within the perimeter
of the tracing of the scale drawing of Big Trout Pond. Count
the shaded squares and record the number.
© 2010 College Board. All rights reserved.
d. How does the area of the shaded squares compare to the area
of the figure?
e. Shade every square that contains some piece of the
perimeter of the figure. How many squares did you shade in
this part? Add the number of squares from Part c and this
part and record the number.
f. How does the total area of the shaded squares now compare
to the area of the figure?
8. Estimate the area of the figure that represents the pond.
Describe how you arrived at your answer
Unit 5 • Geometry
269
ACTIVITY 5.4
Area and Perimeter of Composite Figures
continued
Putting Back the Pieces
SUGGESTED LEARNING STRATEGIES: Group Presentation,
Discussion Group, Self Revision/Peer Revision
My Notes
9. Let each square of the graph paper represent 100 square meters.
Estimate the area of the pond. Show your calculations.
10. How can you make a more accurate estimate of the size of the
pond?
11. Devise a method to find the perimeter of the pond. Use your
method to estimate the perimeter of the pond.
CHECK YOUR UNDERSTANDING
1. Create a shape using 3 or 4 of your
tangrams. Draw its outline and label its
dimensions.
2. What is the area of the shape? Show your
work.
3. What is the perimeter of the shape? Show
your work.
4. Divide the figure below into shapes whose
area you know how to find. Determine the
area of the figure. Show your work.
5. Find the area and perimeter of the
following figure.
2 ft
3 ft
4 ft
8 ft
7 ft
12 ft
6. Find the approximate area of the shape. Each
square on the graph paper represents 2 ft 2.
7. MATHEMATICAL When might you need to
R E F L E C T I O N know how to find the
area of irregular shapes? Explain and give
examples.
270
Springboard® Mathematics with Meaning™ Level 1
© 2010 College Board. All rights reserved.
Write your answers on notebook paper. Show
your work.