Area and Perimeter of Composite Figures Putting Back the Pieces

Transcription

1 Area and Perimeter of Composite Figures SUGGESTED LEARNING STRATEGIES: Use Manipulatives ACTIVITY 5.4 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. 1. Cut out the seven pieces or use a tangram set. Assemble them into the original square tile. Unit 5 Geometry 263

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3 Area and Perimeter of Composite Figures ACTIVITY 5.4 SUGGESTED LEARNING STRATEGIES: Quickwrite, Group Presentation, Think/Pair/Share, Look for a Pattern 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 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. 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 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

4 ACTIVITY 5.4 Area and Perimeter of Composite Figures SUGGESTED LEARNING STRATEGIES: Identify a Subtask, Create Representations, Group Presentation 5. Divide the composite figure below into shapes whose area you know how to find. Use the grid lines as a guide. 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 a. Determine the area of each shape you made. Show your work 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. x b. Give the total area of the composite figure. 6. Compare and contrast your solution with your classmates. 266 Springboard Mathematics with Meaning Level 1

5 Area and Perimeter of Composite Figures ACTIVITY 5.4 SUGGESTED LEARNING STRATEGIES: Marking the Text, Quickwrite, Use Manipulatives 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. Big Trout Pond Unit 5 Geometry 267

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7 Area and Perimeter of Composite Figures ACTIVITY 5.4 SUGGESTED LEARNING STRATEGIES: Quickwrite, Simplify the Problem, Think/Pair/Share, Debriefing, Group Presentation 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. 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

8 ACTIVITY 5.4 Area and Perimeter of Composite Figures SUGGESTED LEARNING STRATEGIES: Group Presentation, Discussion Group, Self Revision/Peer Revision 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 Write your answers on notebook paper. Show your work. 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. 8 ft 2 ft 12 ft 4 ft 3 ft 7 ft 6. Find the approximate area of the shape. Each square on the graph paper represents 2 ft MATHEMATICAL REFLECTION When might you need to know how to find the area of irregular shapes? Explain and give examples. 270 Springboard Mathematics with Meaning Level 1