By Glenda Lappan, James T. Fey, William M. Fitzgerald, Susan N. Friel, Elizabeth Philips
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25. The triangles each have sides of length 6 centimeters, 8 centimeters, and 10 centimeters. Suppose you draw two different triangles. Do they have the same area? qxd 5/16/05 11:54 AM Page 48 Connections For Exercises 26–31, find the area and perimeter of each polygon. Briefly explain your reasoning for Exercises 27, 30, and 31. 26. 28. 30. 48 Covering and Surrounding 27. 29. 31. qxd 5/16/05 11:54 AM Page 49 32. A schooner (SKOON ur) is a sailing ship with two or more masts. The sails of a schooner have interesting shapes.
Qxd 5/16/05 11:51 AM Page 35 29. Suppose a square sheet of paper has a perimeter of 1 meter. a. What is the length of each side (in meters)? b. Suppose you fold the square sheet in half. What new shape would you have? What would the lengths of the shape’s four sides be in meters? What would the perimeter be? 1 c. Suppose you fold over the top 4 of the square. What new shape do you have? What are the lengths of the shape’s four sides in meters? What is the perimeter? 1 d. Suppose you fold over only the top 8 of the square.
A. b. 3 cm 10 cm 8 in. 8 in. c. 2 in. 24 in. 20. 1. Is it possible to have a rectangle that has a smaller perimeter than the rectangles in your table? Explain. 21. Multiple Choice The perimeter of a dog pen is 24 meters. The length 1 is 5 3 meters. What is the width of the dog pen in meters? 1 A. 6 B. 6 3 2 C. 6 D. 7 3 22. 3. Is it possible to have a rectangle that has a greater area than the rectangles in your table? Explain. qxd 5/16/05 11:51 AM Page 33 23. The diagram below represents a field next to Sarah’s house.