5 How to Facts to Know • • • • • • • • • • • • • • • Solve Word Problems with Geometry Basic Geometric Formulas Perimeter • Perimeter is the length around a closed shape. It is computed by adding the length of all the sides of the figure. • The formula for finding the perimeter of rectangles and other parallelograms is P = (l + w) x 2 or P = 2 l + 2 w Area The area of a flat surface is a measure of how much space is covered by that surface. Area is measured in square units. • Area of a Rectangle The area of a rectangle is computed by multiplying the width of one side times the length of the adjoining side. A=lxw • Area of a Triangle A triangle is always one half of a rectangle or a parallelogram. The area of a triangle is computed by multiplying 1/2 of the base times the height of a triangle. A = 1– b x h 2 The area of a rectangle can also be determined by multiplying the base times the height. A=bxh • Area of a Parallelogram The area of a parallelogram is computed by multiplying the base times the height. A=bxh • Area of a Circle To find the area of a circle, multiply π (3.14) times the radius times the radius again. 2 A=πr Circumference The circumference is the distance around a circle. To find the circumference of a circle, multiply π (which always equals 3.14) times the diameter or multiply 2 times π (3.14) times the radius. C = π d or C = 2 π r Volume • The formula for finding the volume of a rectangular prism, such as a box, is to multiply the length times the width times the height. V = l x w x h • The formula for finding the volume of a cylinder is to multiply π (3.14) times the radius squared 2 times the height. V = π x r x h • Volume is always computed in cubic units. Use cubic inches or centimeters when determining volume for small prisms and cylinders, and cubic feet or meters for larger ones. 21 1 Practice • • • • • Recalling Information About Lines and Geometry Directions: Using the information on pages 5 and 6, choose the answer to each question. 1. Geometry comes from two Greek words meaning a. “round” and “equal.” b. “center” and “to measure.” c. “earth” and “center.” d. “earth” and “to measure.” 2. The difference between plane geometry and solid geometry is: e. one is flat and the other is round. f. plane is easier than solid. g. plane has two dimensions and solid has three. h. plane has three dimensions and solid has two. 3. A quadrilateral is a shape with a. sides. b. four straight sides. c. three or more sides. d. long sides. 4. A polygon is a shape with e. curved sides. f. irregular sides. g. four straight sides. h. three or more sides. 5. The beginning and end of a line segment are a. capital letters. b. points. c. line segments that never end. d. arrows. 6. What kind of shape is this? e. polygon f. quadrilateral g. regular h. line segment 7. What kind of shape is this? a. triangle b. quadrilateral c. regular d. line segment 7 ▲ ● Pages 7 and 8 1. d 2. g 3. b 4. h 5. b 6. e 7. b 8. e 9. a 10. f 11. c 12. g 13. d 14. f Pages 12 and 13 1. b 2. f 3. a 4. f 5. b 6. g 7. d 8. e 9. b 10. e 11. c 12. h Page 17 1. 80° 2. 80° 3. 100° 4. 15° 5. g 6. f 7. 110° 8. 70° 9. 70° 10. 180° 11. 360° 12. 30° 13. 30° 14. 150° 15. 30° ■ • • • • • • • • • • • • • • • • • • • • • • Answer Key 6. parallelogram 7. 120 ft. 8. 36 ft. 9. 2.75 ft. 10. 7 ft. 11. 45 ft. 12. 14 ft. Pages 36 and 37 1. 120 ft.2 2. 48 ft.2 3. 400 yds.2 4. 110.25 in.2, 176 in.2 5. 40 ft.2 6. 14.625 ft.2 7. 12 ft.2 8. 6 in.2 9. 6 ft.2 10. 21.85 ft.2 11. 37.1 ft.2 12. 117 in.2 Pages 40 and 41 1. 385 in.3 2. 125 in.3 3. 2,154 in.3 4. 565.2 in.3 5. 400 ft.3 6. 79.507 ft.3 7. 1,846.32 ft.3 8. 427⁄8 ft.3 or 42.875 ft.3 Pages 42 and 43 1. 21 m; 9.5 m2 2. 12 m; 9 m2 3. 36 m; 81 m2 4. 162 m 5. 13.72 m; 4.64 m2 6. 155 cm 7. 25.6 m; 40.87 m2 8. 195 m 9. 84 ft.2 10. 336 ft.2 11. 4 quarts 12. 13.58 m2 13. 43,560 ft.2 14. 4,840 yards2 15. 1.10 acres Pages 20 and 21 1. radius 2. diameter 3. chord 4. circumference 5. 4 ft. 6. 6 in. 7. 9 ft. 8. 8 1⁄2 in. 9. 13⁄4 in. 10. 110 ft. 11. 20.41 miles 12. 5 1⁄2 yds. 13. 452.16 ft.2 14. 615.44 in.2 15. 314 ft.2 Page 25 1. acute 2. equilateral 3. right 4. isosceles 5. obtuse 6. scalene 7. acute 8. isosceles 9. acute 10. scalene 11. acute 12. equilateral Page 29 1. 60° 2. acute and scalene 3. 60° 4. acute and equilateral 5. D = 55° F = 55° 6. 50° 7. c = 2.5'' 8. b = 12' Pages 32 and 33 1. parallelogram 2. trapezoid 3. rhombus 4. rectangle 5. trapezoid 48 16. 3,780,000 pounds 17. A = 5,024 cm2 C = 251 cm 18. 16.75 minutes 19. r = 50 cm A = 7,850 cm2 C = 314 cm time = 20.93 min 20. r = 30 cm A = 2,826 cm2 C = 188.4 cm time = 12.56 min Pages 44 and 45 1. 32 cm2 = 1,024 cm2 2. P = 2(4s) = 16 cm 3. P = 4(4s) = 32 cm 4. A = 4(1 x w) = 16 cm2 5. A = 16(1 x w) = 64 cm2 6. 50° 7. Let side of square A = 1 cm Let the side of square B = 4 cm Area square A = 1 cm Area square B = 16 cm The area of square B is 16 times greater than the area of square A. 8. Area of rectangle = 70 cm x 30 cm = 2,100 cm2 2,100 cm2 + 600 cm2 = 2,700 cm2 30 x 2,700 cm2 = 81,000 cm2 of wood 9. Yes, they have the same area. Since you multiply the base and height, and these two parallelograms use the same numbers, so it doesn’t matter which is the base and which is the height. 5 Practice Geometry at Home • • • • • • • • • • • • • Solving Word Problems with Geometry Geometry is a very important aspect of math around the home. Houses and property are measured in geometric terms. Floor and wall coverings, heating systems, and the water supply all have a geometric component. For this practice page, you need to know the following: • Wallpaper is sold in double rolls totaling 44 square feet. • Carpeting is priced by the square yard. • There are 9 square feet in 1 square yard. • You cannot buy partial rolls of carpeting or wallpaper. Directions: Use the formulas and information on page 21 and the information above to help you solve these word problems. 1. Your mother said you can have new carpeting in your room if you compute the amount of carpeting needed and the cost. The length of your room is 18 1– feet and the width is 17 feet. 2 The cost of one medium grade of carpeting is $20.00 per square yard. A. Compute the number of square feet in the room: __________________ B. Convert square feet to square yards (divide by 9): _________________ C. Compute the cost of carpeting needed (multiply by $20.00): _________ 2. You want to cover one wall of your room with neon-colored wallpaper that costs $25.00 for a double roll containing 44 square feet. The wall is 18 1– feet long and 10 feet high. 2 A. Compute the area of your wall in square feet. _________________ B. Determine how many rolls of wallpaper you need: _____________ C. Compute the cost of the wallpaper: _________________________ 3. Your friend decided to paint the walls and the ceiling of her room with a lovely lavender paint. One gallon of this paint will cover only 400 square feet and costs $17.99 a gallon. These are the dimensions of her room: • Wall 1—21 1– feet long and 11 1– feet high • Wall 3—21 1– feet long and 11 1– feet high 4 2 4 2 • Wall 2—20 feet long and 11 1– feet high • Wall 4—20 feet long and 11 1– feet high 2 2 • Ceiling—21 1– feet long and 20 feet wide 4 A. Compute the area of each wall and ceiling in square feet. Wall 1 ______ Wall 2 ______ Wall 3 ______ Wall 4 ______ Ceiling _________ B. Compute the total area in square feet: _________________________________ C. Determine how many gallons of paint are needed: _______________________ D. Compute the total cost of the paint: ___________________________________ 22 5 Practice Neighborhood Jobs • • • • • • • • • Solving More Word Problems with Geometry You need money to supplement your allowance. You decide to pick up some jobs at home and in the neighborhood so you can buy some necessities such as a scooter, a mountain bike, and a boom box. Directions: Use the formulas and information on page 21 to help you solve these word problems. 1. Your dad agrees to pay you for mowing the front and back lawn. He will pay you $0.01 a square foot. The front lawn is 62 feet long and 38 feet wide. 5. A neighbor down the street offers to pay you $0.15 a square foot to paint his fence which is 103 feet long and 6.25 feet high. He will supply the paint. A. What is the square footage? _________ B. How much will you be paid? ________ A. What is the square footage? __________ B. How much will you be paid? _________ 2. Your dad will pay you $0.03 a linear foot for trimming the edge of this lawn. 6. Your favorite uncle offers to pay you $0.18 a square foot to paint his board fence. It is 8 1– feet high and 26 feet long. 2 A. What is the square footage? __________ B. How much will you be paid? _________ A. What is the perimeter of the lawn? ____ B. How much will you be paid? _________ 3. The back lawn is shaped like a parallelogram. The base is 36 feet and the height is 31 feet. 7. A neighboring mother wants you to paint a dodge ball court with a 6-foot radius on her driveway. A. What is the square footage? __________ B. How much will you be paid? _________ A. What is the circumference of the court? __________ B. What is the area in square feet of the court? _________ 4. Your next-door neighbor offers to pay you the same price for edging and mowing his circular lawn which has a radius of 5.5 feet. A. What is the circumference of the lawn? __________ B. How much will you be paid for edging? __________ C. What is the area of the lawn in square feet? _________ D. How much will you be paid for mowing it? ___________ Extension • Measure and compute the perimeter and area of your lawn. • Measure and compute the perimeter and area of a neighbor’s lawn. 23 5 Practice • • • • • • • • • • • • • • • • • Solving Even More Word Problems with Geometry Directions: Use the formulas and information on page 21 to help you solve these word problems. 1. You decide to start your own sidewalk business after school selling candy bars. The candy bars come packed in cartons which are 1 foot long, 1 foot wide, and 1 foot high (a cubic foot). How many of these cartons could you pack into your closet which is 5 feet long, 4 feet wide, and 12 feet high? _______________ 2. Your bedroom is 20 feet wide, 18 1– feet long, and 11 feet high. How many cubic feet of space are 2 in your bedroom? __________________ 3. The circular top of your water heater has a radius of 9 inches. The height of the cylinder is 8 feet 5 inches. How many cubic inches of water will the water heater hold? _________________ 4. A can of cleanser has a radius of 4.5 cm and a height of 22.3 cm. How many cubic centimeters of cleanser will the can hold? _______________ 5. A closet in your parent’s bedroom is 9 1– feet long, 3 1– feet wide, and 12 feet high. How many 4 3 cubic feet of space does it have? _______________ 6. This is a diagram of the living room in a house. Compute the number of cubic feet in the room. (Hint: Do the problem in two sections.) _______________ 51 feet 36 1 – feet The height of the ceiling is 10 feet. 2 16 1 – feet 2 28 feet 7. A city water tower is 83 feet high with a radius of 25 feet. How many cubic feet of water can be stored in the tower? ________________ 8. A cubic foot of water weighs 62.38 pounds. What is the weight of the water that can be stored in the water tower in problem #7? _______________ 9. One cubic foot of water equals 7.48 gallons. How many gallons of water can be stored in the water tower in problem #7? _______________ 10. How many cubic inches of water will fit into a hose which is 50 feet long and has a radius of 1– inch? _________________ 2 11. One silo or elevator for storing grain has a radius of 15 feet and is 120 feet high. How many cubic feet of grain can be stored in it? _______________ 24 • • • • • • • • • • • • • • • • • • • • • • Answer Key Page 6 5. 405 in.2 1. 5 11⁄16" 6. 49.14 m2 2. 2 5⁄16" 7. 116.39 cm2 3. 6 3/4" 8. 86.45 m2 4. 6 7/16" Page 16 5.–18. Answers will vary. 1. 50.24 m2 Pages 7 and 8 2. 78.5 cm2 Answers will vary. 3. 314 cm2 4. 452.16 cm2 Page 10 5. 1,256 cm2 1. 18.2 cm 6. 615.44 ft.2 2. 26.2 cm 7. 706.5 in.2 3. 131⁄2 cm 8. 1,962.5 m2 4. 161⁄2 ft. 5. 151⁄4 in. Page 18 6. 183⁄8 cm. 1. 105 m3 7.–10. Answers will vary. 2. 720 ft.3 3. 343 cm3 Page 11 4. 165 in.3 1. 15.6 cm 5. 240 yd.3 2. 111⁄4 in. 6. 67.032 m3 3. 24.4 m 7. 92.736 m3 4. 183⁄4 ft. 8. 694.512 cm3 5. 74.4 m 9. 1,728 ft.3 6. 64 yd. 10. 86 6/8 ft.3 7. 137.4 cm 8. 105.3 m Page 19 1. 351.68 m3 Page 12 2. 169.56 cm3 1. 19.1 m 3. 282.6 cm3 2. 22.6 m 4. 18.84 in.3 3. 26 in. 5. 50,240 cm3 4. 201⁄2 ft. 6. 1,538.6 ft.3 5. 25.12 m 6. 37.68 in. Pages 20–23 7. 31.4 cm Answers will vary. 8. 21.98 m Page 24 Page 14 1. 6 lbs. 4 oz. 2 1. 41 m 2. 1 ton 300 lbs. 2. 126 yd.2 3. 4,000 cassettes 3. 67.5 cm2 4. 100 pills 4. 6.08 m2 5. 100,000 pills 2 5. 34 ft. 6. 2,000 dictionaries 6. 16 1/4 in.2 7. 12,000 staplers 7. 3,680 m2 8. 100 people 8. 7,500 mm2 9. 500 mg or 1/2 g 10. 220 kg Page 15 11. 4,400 kg 1. 24 ft.2 12. 2,200 clips 2. 45 yd.2 13. 6,400 calculators 3. 11.66 cm2 14. 40 cameras 4. 27.72 cm2 Page 26 1. 8 fl. oz. 2. 16 fl. oz. 3. 32 fl. oz. 4. 48 fl. oz. 5. 64 fl. oz. 6. 72 fl. oz. 7. 32 fl. oz. 8. 64 fl. oz. 9. 160 fl. oz. 10. 96 fl. oz. 11. 4 qt. 12. 16 qt. 13. 128 fl. oz. 14. 60 qt. 15. 1,920 fl. oz. 16. 16 fl. oz. 17. 48 fl. oz. 18. 112 fl. oz. 19. 40 pints 20. 176 cups 21. 120 pints 22. 1,280 fl. oz. 23. 34 cups 24. 176 fl. oz. 25. 344 fl. oz. Page 27 1. 30 mL 2. 240 mL 3. 1,000 mL 4. 960 mL 5. 40 mL 6. 480 mL 7. 3,840 mL 8. 3.84 L 9. 38.4 L 10. 69.1 L 11. 960 L 12. 96 L 13. 96 L 14. 1920 15. 360 L Page 28 1. 2 qt. 2. 12 mL 3. 80 mL 4. 336 mL 5. 50 pennies 6. 432 mL 47 7. 8. 9. 10. 11. 12. 24 fl. oz. 384 mL 128 quarters 19.2 L 8 times 48 cups Page 30 1. 40° acute 2. 120° obtuse 3. 180° straight 4. 90° right 5. 50° acute 6. 130° obtuse 7. 250° reflex 8. 215° reflex 9. 90° right 10. 80° acute Page 31 1. <BAC = 100° 1. <CBA = 35° 1. <ACB = 45° 1. ▲ABC = 180° 2. <CDE = 50° 1. <ECD = 70° 1. <DEC = 60° 1. ▲DEC = 180° 3. <LMN = 90° 1. <MNL = 30° 1. <MLN = 60° 1. ▲LMN = 180° 4. <MNO = 25° 1. <OMN = 65° 1. <MON = 90° 1. ▲MNO = 180° 5. <XYZ = 60° 1. <ZXY = 60° 1. <YZX = 60° 1. ▲XYZ = 180° 6. <WPO = 154° 1. <POW = 11° 1. <PWO = 15° 1. ▲WPO = 180° ? ? ? Page 6 1. change subtraction $2.12 2. money spent multiplication $36.64 3. split evenly division 28 cards 4. amount needed subtraction $10.33 5. total cost addition $129.17 6. how much saved subtraction $2.21 7. total cost multiplication $41.58 Page 7 1. change subtraction $16.11 2. % discount multiplication $59.80 3. total cost addition $50.73 4. times as much multiplication $5,325 5. average division 11.03 miles 6. total cost addition $1,342.97 7. times as much multiplication $350.10 8. total addition 125.3 miles Page 8 1. how much change subtraction $8.05 • • • • • • • • • • • • • • • • • • • • • • Answer Key 2. how much saved subtraction $6.95 3. product multiplication $113.85 4. how much left subtraction $25.41 5. split evenly division $1.59 6. share evenly division 27 CDs 7. discount multiplication $3.19 8. difference subtraction $3.11 Page 12 1. multiplication $22.68 2. addition $8.97 3. multiplication $59.67 4. addition $13.46 5. division $17.04 6. subtraction $2.70 Challenge: $70.20; 1 large cola, 1 Double Bean Burrito, 1 Tornado Taco; $0.39 Page 14 1. 7/12 miles 2. 5/12 miles 3. 2 2/3 miles 4. 1/3 mile 5. 1 1/6 miles 6. 8 miles 7. 1 1/4 miles 8. 4 5/18 miles 9. 1/2 mile 10. 26 2/3 miles Page 10 1. addition $34.42 2. subtraction $2.55 3. subtraction $7.50 4. addition $40.47 5. subtraction $3.50 6. addition $78.41 7. addition Answers will vary. Extension: Answers will vary. Page 15 1. 3/4 pizza 2. 10 cups 3. 3 3/4 pizzas 4. 1 1/2 pizzas 5. 1/2 pizza 6. 1/10 cake 7. 15/16 cake 8. 14 cups 9. 5/8 pizza 10. 81 ounces 11. 338 ounces 12. 1 1/2 ounces Page 11 1. multiplication $45.00 2. division $3.75 3. multiplication $126.50 4. multiplication $99.80 5. multiplication $119.25 6. division $1.79 Challenge: $11.25; $8.75 Extension: 4 2/3 pizzas Page 16 1. 33 3/4 miles 2. 39/40 mile 46 3. 7/10 mile 4. 1/2 lb. 5. 14 2/3 miles 6. 9 lbs. 7. 4 5/3 miles 8. 1 13/40 sec. 9. 12 3/8 miles 10. 7 17/24 miles Extension: Answers will vary. Page 18 1. $62.29; $237.71 2. $77.50; $160.21 3. $11.88; $148.33 4. $7.46; $29.82; $118.51 5. $57.94; $60.57 6. $10.00; $60.00; $0.57 7. $299.43 8. no Page 19 1. 60% 2. 24 shots 3. 71% or 71.4% 4. 17 shots 5. 89% or 89.3% 6. 19 shots 7. 94% or 94.4% 8. 65% or 64.7% 9. 64% or 63.9% 10. 4 shots Challenge: Answers will vary. Page 20 1. 0.625 gallons 2. 25.2 lbs. 3. 4.4 oz. 4. 43.2 lbs. 5. 2.4 qts. 6. 114.7 lbs. 7. 19.5 lbs. 8. 3.75 or 3 3/4 times 9. 56% or 55.6% 10. 41% Page 22 1. A. 314.5 sq. ft. B. 34.9 or 35 sq. yd. • • • • • • • • • • • • • • • • • • • • • • Answer Key ? ? ? C. $698.00 or $700.00 2. A. 185 sq. ft. B. 5 rolls C. $125 3. A. 244 3/8 sq. ft. 230 sq. ft.; 244 3/8 sq. ft.; 230 sq. ft.; 425 sq. ft. B. 1,373 3/4 sq. ft. or 1,374 sq. ft. C. 4 gallons D. $71.96 Page 23 1. A. B. 2. A. B. 3. A. B. 4. A. B. C. D. 5. A. B. 6. A. B. 7. A. B. 2,356 sq. ft. $23.56 200 ft. $6.00 1,116 sq. ft. $11.16 34.54 ft. $1.04 94.99 sq. ft. $0.95 643.75 sq. ft. $96.56 221 sq. ft. $39.78 37.68 ft. 113.04 sq. ft. Extension: Answers will vary. Page 24 1. 240 cartons 2. 4,070 cu. ft. 3. 25,688.34 cu. in. 4. 1,417.95 cu. cm 5. 370 cu. ft. 6. 14,820 cu. ft. 7. 162,887.5 cu. ft. 8. 10,160,922 lb. 9. 1,218,398.5 gallons 10. 471 cu. in. 11. 84,780 cu.ft. Page 26 1. $45.60 2. $34.13 3. $104.65 4. 5. 6. 7. 8. 9. $43.51 $32.95 $29.25 $36.86 $30,555.64 Monday and Tuesday = Saturday 10. $17,111.16 11. $12,473.53 4. 5. 6. 7. Page 27 1. $101.47 2. $12.27 3. You could buy the DVD player; $179.67 $5.96 change 4. $786.15 5. The traditional machine/phone is $11.24 cheaper. 6. $19.20 7. $49.76 8. Boom Box City $25.46 less 9. $16.30 10. 25% 8. 0 quarters, 2 half dollars 6, 9, 12, 15, 18 300, 350, 400, 450, 500 3 footballs, 6 tennis balls, 3 baseballs, 2 basketballs Jack is 26 years old; Dad is 52 years old Marie is 22 years old; Mother is 44 years old Page 31 1. $360.00 2. 2,700 beads 3. 240 total 16 skirts 32 jeans 64 shorts 128 blouses 4. $372.00 total Elaine $12.00 Christina $24.00 Alyse $48.00 Doreen $96.00 Melissa $192.00 5. James 2 years old Raymond 3 years old Brett 4 1/2 years old John 6 years old Robert 11 years old Page 28 1. 22.86 miles per day 2. 4 hr. 24 min. 3. 3 hr. 20 min. 4. 40 m.p.h. 5. 1 mile per minute 6. $21.00 7. $3.20 8. $0.82 9. $46.74 Page 32 1. 3 hr. 2 min. 2. 31 games 3. 81 times 4. 30 names 5. 20 points on 8th game; 35 points on 14th game 6. 35 players are 13 years old Page 30 1. 6 tops/4 skorts 2. 3 pennies, 3 nickels, 0 dimes, 3 quarters, 3. A. 1 penny, 0 nickels, 4 dimes, 4 quarters, 0 half dollars B. 1 penny, 4 nickels, 2 dimes, Page 34 1. n = 36–23 n = 13 13 years old 2. n = (4 x 15) + 2 47 n = 62 62 CDs 3. n = 216–122 n = 94 94 lb. 4. n = 25 x .60 n = 15 15 shots 5. n = 22 – 7 n = 15 15 minutes 6. n = 1,145 – 316 n = 829 829 words 7. n = 88 x 3/4 n = 66 66 minutes Extension: Answers will vary. Page 35 1. n + (n + 28) = 50 2n + 28 = 50 n = 11 Mother is 39 years old. Sarah is 11 years old. 2. n + (n + 140)= 336 2n + 140= 336 n = 98 Joe weighs 98 lbs. Dad weighs 238 lbs. 3. n + 4n + 22 = 122 n = 25 Melissa has $25.00. Christina has $97.00. 4. n + 2n = 669 3n = 669 n = 223 John read 223 words. Joseph read 446 words. 5. n + 4n = 15 5n = 15 n=3 Nicholas is 3 years old. Norman is 12 years old. 10 Word Problems • • • • • • • • • • • • • • • • Real Life Geometry The students at Wood Hill Elementary were surprised one day in gym class when the coach handed out a math test. “What’s going on?” they asked. “Good athletes have to be good students, too,” said the coach. “You don’t want to be disqualified from a team because of poor grades. Answer these questions.” He gave them each sheet of paper. 1. The volleyball net is 1 m wide and 9.50 m long. What are the perimeter and the area of the net? perimeter = ____________ area = ____________ 2. The service area in volleyball is 3 m long and 3 m wide. What is the perimeter and the area of the service area? perimeter = ____________ area = ____________ 3. The volleyball court is 18 m long and 9 m wide. It is divided into two halves. What are the perimeter and the area of each half? perimeter = ____________ area = ____________ 4. Tiffany runs 3 times around the volleyball court. How far does she run? ____________ 5. The badminton net is 0.76 m wide and 6.10 m long. What are the perimeter and area of the net? perimeter = ____________ area = ____________ 6. The badminton net is 1.55 m high (1 m = 100 cm). What is its height in centimeters? ____________ 7. The badminton court is 13.40 m long and 6.10 m wide. It is divided into two halves. What is the perimeter of each half? ____________ How many square meters of material would it take to cover one half? ____________ 8. Dan runs 5 times around the badminton court. How far does he run? ____________ Ira has agreed to do a project for his father in exchange for a new snowboard this winter. Ira needs to paint the garden shed in his backyard. His father needs to buy the paint for the shed and has asked Ira to measure the size of each wall to determine the amount of paint he should purchase. There are four walls to the shed. 9. After measuring the walls, Ira has determined that each wall is 7 feet high and 12 feet long. What is the area of each wall? ____________ 10. What is the total area of the walls around the shed? ____________ 11. If a quart of paint covers 100 square feet, how many quarts of paint must Ira’s father purchase? ____________ 12. Dan O’Leary has decided to plant a garden. He wants to make it 10.1 m long and 4.2 m wide. However, in order to keep the rabbits out, Dan needs a fence surrounding the garden. He decides to make the fence 11.2 m long and 5.0 m wide. What is the area between the fence and the garden? ____________ (Hint: Find the area for the garden. Then, find the area of the space surrounded by the fence.) 42 10 Word Problems • • • • • • • • • • • • • • • • Real Life Geometry The rod is an old unit of measurement of length. A rod is 16 1/2 feet long. A square rod is a square plot of ground. Each side of the plot is 16 1/2 feet long. An acre is 160 square rods. 13. How many square feet are in one acre? ____________ 14. How many square yards are in one acre? ____________ 15. A football field is 160 feet wide and 300 feet from goal line to goal line. What is the area of the football field in acres? (round to the nearest hundredth) ____________ 16. Mr. Anderson is a farmer. He has a 300-acre field. He expects to harvest about 225 bushels of corn per acre. A bushel of corn weighs about 56 pounds. How many pounds of corn would Tom get from his field? ____________ Mr. Peterson is a math teacher. Dinner at his house is unusual. One night, after a pizza was delivered, he posed the following questions to his hungry family. “Before we eat this delicious pizza, let’s answer a few interesting questions,” he said. Everyone groaned. “The radius of a regular pizza is 40 cm. Now, listen closely to my questions.” 17. Find the area and the circumference of the pizza. area = _______ circumference = _______ 18. If an ant walked 1 cm in 4 seconds, how long would it take for the ant to walk the circumference? ____________ 19. Repeat question #18 assuming the radius of the pizza is increased by 25%. Find the following measurements: radius = _______ area = _______ circumference = _______ ant’s time = _______ 20. Repeat question #18 assuming the radius of the pizza is decreased by 25%. Find the following measurements: radius = _______ area = _______ circumference = _______ ant’s time = _______ 43 11 • • • • • • • • • • • • Carpenters and Pyramids Brain Teasers Directions: Answer these brain teaser questions. 1. Four strips of paneling 40 cm long and 4 cm wide are arranged to form a square, like a picture frame. (Note: The ends of the strip of paneling will overlap.) What is the area of the inner square in square cm? ____________ It’s “Challenge Day” in Mr. Peterson’s math class. “Take out a sheet of paper,” he says. “Now, draw a 2 cm x 2 cm square. Listen closely. 2. What is the equation for finding the perimeter of a square that is twice the size of the original square? _________________________ 3. What is the equation for finding the perimeter of a square that is four times the size of the original square? _________________________ 4. What is the equation for finding the area of a square that is twice the size of the original square? _________________________ 5. What is the equation for finding the area of a square that is four times the size of the original square? _________________________ 6. In the following diagram of the front view of the Great Pyramid, the measure of PRQ is 120° degrees, and the measure of PST is 110° degrees. What is the measure of RPS in degrees? _________________________ P Q R (Hint: The sum of the angles in a triangle is 180 degrees. A straight line is 180 degrees. Use the known angles to find the unknown angles. See Unit 3 on supplementary angles to help you solve the problem.) S T 7. One side of square B is four times the length of one side of square A. How many times greater is the area of square B than the area of square A? _________________________ B A 44 11 Brain Teasers • • • • • • • • • • • • Carpenters and Pyramids 8. Two carpenters decided to design desks for students at James Hart Junior High. The dimensions of the desks are as shown. How much wood in cm2 would they need for 30 desks? __________ 70 cm 30 cm 20 cm 20 cm (Hint: What is the area of one desk? Find the area of each part and add all the areas to find the total area. If there are 30 desks, how much wood in square centimeters is needed?) 9. Do these parallelograms have the same area? How do you know? __________________________ _______________________________________________________________________________ _______________________________________________________________________________ 2 cm 5 cm 2 cm 5 cm (Hint: Review the formula for finding the area of a parallelogram.) 45 ▲ ● Pages 7 and 8 1. d 2. g 3. b 4. h 5. b 6. e 7. b 8. e 9. a 10. f 11. c 12. g 13. d 14. f Pages 12 and 13 1. b 2. f 3. a 4. f 5. b 6. g 7. d 8. e 9. b 10. e 11. c 12. h Page 17 1. 80° 2. 80° 3. 100° 4. 15° 5. g 6. f 7. 110° 8. 70° 9. 70° 10. 180° 11. 360° 12. 30° 13. 30° 14. 150° 15. 30° ■ • • • • • • • • • • • • • • • • • • • • • • Answer Key 6. parallelogram 7. 120 ft. 8. 36 ft. 9. 2.75 ft. 10. 7 ft. 11. 45 ft. 12. 14 ft. Pages 36 and 37 1. 120 ft.2 2. 48 ft.2 3. 400 yds.2 4. 110.25 in.2, 176 in.2 5. 40 ft.2 6. 14.625 ft.2 7. 12 ft.2 8. 6 in.2 9. 6 ft.2 10. 21.85 ft.2 11. 37.1 ft.2 12. 117 in.2 Pages 40 and 41 1. 385 in.3 2. 125 in.3 3. 2,154 in.3 4. 565.2 in.3 5. 400 ft.3 6. 79.507 ft.3 7. 1,846.32 ft.3 8. 427⁄8 ft.3 or 42.875 ft.3 Pages 42 and 43 1. 21 m; 9.5 m2 2. 12 m; 9 m2 3. 36 m; 81 m2 4. 162 m 5. 13.72 m; 4.64 m2 6. 155 cm 7. 25.6 m; 40.87 m2 8. 195 m 9. 84 ft.2 10. 336 ft.2 11. 4 quarts 12. 13.58 m2 13. 43,560 ft.2 14. 4,840 yards2 15. 1.10 acres Pages 20 and 21 1. radius 2. diameter 3. chord 4. circumference 5. 4 ft. 6. 6 in. 7. 9 ft. 8. 8 1⁄2 in. 9. 13⁄4 in. 10. 110 ft. 11. 20.41 miles 12. 5 1⁄2 yds. 13. 452.16 ft.2 14. 615.44 in.2 15. 314 ft.2 Page 25 1. acute 2. equilateral 3. right 4. isosceles 5. obtuse 6. scalene 7. acute 8. isosceles 9. acute 10. scalene 11. acute 12. equilateral Page 29 1. 60° 2. acute and scalene 3. 60° 4. acute and equilateral 5. D = 55° F = 55° 6. 50° 7. c = 2.5'' 8. b = 12' Pages 32 and 33 1. parallelogram 2. trapezoid 3. rhombus 4. rectangle 5. trapezoid 48 16. 3,780,000 pounds 17. A = 5,024 cm2 C = 251 cm 18. 16.75 minutes 19. r = 50 cm A = 7,850 cm2 C = 314 cm time = 20.93 min 20. r = 30 cm A = 2,826 cm2 C = 188.4 cm time = 12.56 min Pages 44 and 45 1. 32 cm2 = 1,024 cm2 2. P = 2(4s) = 16 cm 3. P = 4(4s) = 32 cm 4. A = 4(1 x w) = 16 cm2 5. A = 16(1 x w) = 64 cm2 6. 50° 7. Let side of square A = 1 cm Let the side of square B = 4 cm Area square A = 1 cm Area square B = 16 cm The area of square B is 16 times greater than the area of square A. 8. Area of rectangle = 70 cm x 30 cm = 2,100 cm2 2,100 cm2 + 600 cm2 = 2,700 cm2 30 x 2,700 cm2 = 81,000 cm2 of wood 9. Yes, they have the same area. Since you multiply the base and height, and these two parallelograms use the same numbers, so it doesn’t matter which is the base and which is the height.

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