Name: Class: Date: ID: A Area and Perimeter Short Answer 1. The squares on this grid are 1 centimeter long and 1 centimeter wide. Outline two different figures with an area of 12 square centimeters and a perimeter of 16 centimeters. 2. Find the area and perimeter of this rectangle. Explain how you found your answers. 1
Name: ID: A 3. Jason is planning to redecorate his bedroom. He measured the room and made this rough sketch. a. Jason is planning to buy paint for the walls and ceiling. Will he need to find the perimeter or area to figure out how much paint to buy? What unit of measure should he use? b. To determine how much new carpet to buy, will Jason need to find the perimeter or area? What unit of measure should he use? c. Jason also needs baseboard for around the bottom of the walls. Will he need to find the perimeter or area to figure out how much baseboard to buy? What unit of measure should he use? d. How much carpeting does Jason need? Show how you found your answer. e. How much baseboard does Jason need? Show how you found your answer. f. If a gallon of paint covers 350 square feet, how much paint does Jason need for the walls and ceiling? 4. Find the area and the perimeter of each of the four shapes below. a. b. c. d. 2
Name: ID: A 5. Susan is helping her father measure the living room floor because they want to buy new carpeting. The floor is in the shape of a rectangle with a width of 10 feet and a length of 14 feet. a. Draw a sketch that shows the shape of the floor and label the length and width. b. If the carpeting costs $1.75 per square foot, how much will it cost to buy the exact amount of carpeting needed to carpet the living room? Explain your reasoning. c. Baseboard needs to be installed along the base of the walls to hold the carpeting in place. Baseboard costs $2.35 per foot. There is one 6-foot wide entry into the living room that does not need baseboard. Find the exact amount of baseboard needed and the exact cost. Explain your reasoning. 6. Ellen drew a rectangle. She says the area of her rectangle is 7 square units and the perimeter is 16 units. Could Ellen be correct about the perimeter and area of her rectangle? Explain why or why not. 7. Use the diagram below to answer the following questions. (All angles in the diagram are right angles.) a. What is the perimeter of the figure? b. What is the area of the figure? c. Explain how you found your answers for parts (a) and (b). 3
Name: ID: A 8. Find the area and perimeter of each figure below a. b. c. d. e. f. 9. Find the area and perimeter of each of the following rectangles. 10. Find the area of the rectangle with length 30 inches and width 37 inches. 11. Find the area of the rectangle with length 43 inches and width 45 inches. 12. Find the area of the rectangle with length 13 inches and width 25 inches. 13. Find the area of the rectangle with length 50 inches and width 34 inches. 14. Find the area of the rectangle with length 45 inches and width 41 inches. 15. Find the area of the rectangle with length 26 inches and width 7 inches. 16. Find the perimeter of the rectangle with length 97 inches and width 17 inches. 17. Find the perimeter of the rectangle with length 95 inches and width 87 inches. 18. Find the perimeter of the rectangle with length 15 inches and width 68 inches. 4
Name: ID: A 19. Find the perimeter of the rectangle with length 19 inches and width 52 inches. 20. Find the perimeter of the rectangle with length 72 inches and width 67 inches. 21. Find the perimeter of the rectangle with length 50 inches and width 94 inches. 22. Each pail of plaster covers 97 square feet of ceiling. How many pails of plaster would you need to buy to cover the ceiling of a room with walls 14 feet long? 23. Each pail of plaster covers 97 square feet of ceiling. How many pails of plaster would you need to buy to cover the ceiling of a room with walls 20 feet long? 24. Each pail of plaster covers 97 square feet of ceiling. How many pails of plaster would you need to buy to cover the ceiling of a room with walls 11 feet long? 25. Find the area of the parallelogram. Find the area of a parallelogram with base b and height h. 26. b = 95 cm h = 9.6 cm 27. b = 82 cm h = 16.6 cm 28. Find the area of the parallelogram. Not drawn to scale 5
Name: ID: A 29. Find the area of the parallelogram with base 471.5 cm and height 21.3 cm. Multiple Choice Identify the choice that best completes the statement or answers the question. 30. If the width of a rectangle is tripled, what will be the effect on its area? a. The area will remain the same. c. The area will be 3 times as great. b. The area will be 9 times as great. d. The area will be 6 times as great. 6
Area and Perimeter Answer Section SHORT ANSWER 1. ANS: Answers will vary. Possible answers: REF: Covering and Surrounding Check-Up KEY: area of a rectangle area and perimeter perimeter 2. ANS: Area: 20 sq. cm, Perimeter: 18 cm; Possible explanation: I multiplied 5 by 4 to find the area. To find the perimeter I added the length and the width, then multiplied this answer by 2, in order to account for both lengths and both widths. REF: Covering and Surrounding Check-Up KEY: dimension area of a rectangle perimeter 1
3. ANS: a. area, square feet b. area, square yards (or square feet) c. perimeter, feet d. The room is 3 yards (9 feet) by 4 yards (12 feet), so 3 4 = 12 square yards of carpet are needed (108 square feet is also correct). e. (9 + 12) 2 = 42 feet of baseboard (Some students may argue for less than 42 feet-say, 39 feet-because of the door opening not needing baseboard. This is a reasonable answer as well.) f. Possible answer: Two of the walls need 12 8 = 96 square feet of paint, two of the walls need 9 8 = 72 square feet of paint, and the ceiling needs 12 9 = 108 square feet of paint, so there is (96 2) + (72 2) + 108 = 444 square feet to cover. This would require 444 350 = about 1.27 gallons of paint, so you would need 1 1 2 or 2 gallons (if the paint came only in full gallons). REF: Covering and Surrounding Question Bank KEY: dimension area of a rectangle area perimeter 4. ANS: a. P = 22 units, A = 28 square units b. P = 28 units, A = 33 square units c. P = 23 units, A = 33 square units Ê d. P = 17.5 units, A = 17.875 17 7 ˆ Ë Á 8 square units REF: Covering and Surrounding Additional Practice Investigation 1 TOP: Problem 1.1 Understanding Area and Perimeter KEY: area and perimeter 5. ANS: a. Students should draw and label a 10 14 rectangle. b. $245 c. $98.70 REF: Covering and Surrounding Additional Practice Investigation 1 TOP: Problem 1.2 Finding Area and Perimeter KEY: area perimeter 2
6. ANS: Ellen could be correct if she drew a 1 7 rectangle. REF: Covering and Surrounding Additional Practice Investigation 1 TOP: Problem 1.2 Finding Area and Perimeter KEY: area of a rectangle area and perimeter perimeter 7. ANS: a. 28 centimeters b. 27 square centimeters c. Possible answers: Subdivide the figure into rectangles to find the area and to help find the perimeter. REF: Covering and Surrounding Additional Practice Investigation 1 KEY: dimension area perimeter area of an irregular figure 8. ANS: a. Area: 16 cm 2, Perimeter: 16 cm b. Area: 10 cm 2, Perimeter: 16 cm c. Area: 12 cm 2, Perimeter: 16 cm d. Area: 8 cm 2, Perimeter: 16 cm e. Area: 7 cm 2, Perimeter: 16 cm f. Area: 6.25 cm 2, Perimeter: 16 cm REF: Covering and Surrounding Additional Practice Investigation 1 KEY: dimension area perimeter area of a rectangle area of an irregular figure 3
9. ANS: a. Area: 21 in 2, Perimeter: 20 in b. Area: 12.25 in 2, Perimeter: 14 in c. Area: 200 cm 2, Perimeter: 66 cm d. Area: 32.83 cm 2, Perimeter: 23.2 cm REF: Covering and Surrounding Additional Practice Investigation 1 TOP: Problem 1.2 Finding Area and Perimeter KEY: area area of a rectangle area and perimeter perimeter 10. ANS: 1,110 in. 2 11. ANS: 1,935 in. 2 12. ANS: 325 in. 2 13. ANS: 1,700 in. 2 KEY: area rectangle KEY: area rectangle KEY: area rectangle KEY: area rectangle 4
14. ANS: 1,845 in. 2 15. ANS: 182 in. 2 16. ANS: 228 in. 17. ANS: 364 in. 18. ANS: 166 in. 19. ANS: 142 in. KEY: area rectangle KEY: area rectangle KEY: perimeter rectangle KEY: perimeter rectangle KEY: perimeter rectangle KEY: perimeter rectangle 5
20. ANS: 278 in. 21. ANS: 288 in. 22. ANS: 3 pails KEY: perimeter rectangle KEY: perimeter rectangle KEY: area rectangle word problem problem solving 23. ANS: 5 pails KEY: area rectangle word problem problem solving 24. ANS: 2 pails KEY: area rectangle word problem problem solving 6
25. ANS: 1,200 ft 2 TOP: Problem 1.3 Formulas for Area and Perimeter KEY: area base height parallelogram geometry 26. ANS: 912 cm 2 TOP: Problem 1.3 Formulas for Area and Perimeter KEY: area base height parallelogram geometry 27. ANS: 275.56 cm 2 TOP: Problem 1.3 Formulas for Area and Perimeter KEY: area base height parallelogram geometry 28. ANS: 170 cm 2 TOP: Problem 1.3 Formulas for Area and Perimeter KEY: area parallelogram base height 29. ANS: 10,042.95 cm 2 TOP: Problem 1.3 Formulas for Area and Perimeter KEY: area base height parallelogram STA: 6WA 1.5.2c STA: 6WA 1.5.2c STA: 6WA 1.5.2c STA: 6WA 1.5.2c STA: 6WA 1.5.2c 7
MULTIPLE CHOICE 30. ANS: C REF: Covering and Surrounding Multiple Choice KEY: dimension area area of a rectangle angle 8