Answers for Chapter 5 Masters

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1 Answers for Chapter 5 Masters Scaffolding Answers Scaffolding for Getting Started Activity p. 53 B. By counting the squares found in each shape. The area of the green rectangle is 10 cm 2. C. The area of the green rectangle is the same as the total area of the yellow triangles (10 cm 2 ). D. The total area of the two yellow triangles is 10 cm 2, which is the same as the green rectangle. The area of one yellow triangle is 5 cm 2. I know this because one triangle has half of the area of the green rectangle. E. The end of the parallelogram has the same area as a yellow triangle. The area of the red rectangle is 30 cm 2. The area of the red parallelogram is 30 cm 2. F. The area of one yellow triangle is 5 cm 2. The area of two yellow triangles is 10 cm 2. The area of the rectangle made of two yellow triangles and one blue triangle is 20 cm 2. G. The total area of the two yellow triangles is 10 cm 2. Since the two yellow triangles cover the entire blue triangle, I know that the area of the blue triangle is also 10 cm 2. Scaffolding for Do You Remember? Questions 1 & 4 p m = 1 km, 100 cm = 1 m, cm = 1 km, 10 mm = 1 cm, 1000 mm = 1 m a) 1 km = cm c) 4 m = 4000 mm 1 km > 1000 cm 40 mm < 4 m b) 3 m = 300 cm d) 89 m = 8900 cm 300 cm = 3 m 89 m > 890 cm 4. a) Perimeter = 7 m + 7 m + 8 m + 8 m Area = l w = 30 m = 7 m 8 m = 56 m 2 b) Perimeter = 30 cm + 30 cm + 60 cm + 30 cm + 90 cm + 60 cm = 300 cm Area (rectangle 1) = l x w Area (rectangle 2) = l w = 30 cm 30 cm = 30 cm 90cm = 900 cm 2 = 2700 cm 2 Area of shape = Area (rectangle 1) + Area (rectangle 2) = 900 cm cm 2 = 3600 cm 2 Scaffolding for Lesson 5.1, Question 14 p Room Parallelogram Base Height Area entrance red 4 m 1 m 4 m 2 kitchen blue 6 m 2 m 12 m 2 living room yellow 6 m 4 m 24 m 2 bathroom purple 4 m 2 m 8 m 2 bedroom green 6 m 2 m 12 m 2 62 Chapter 5: 2-D Measurement Copyright 2006 by Thomson Nelson

2 Chapter Test Master 1. a) Perimeter = (2 2.5 m) + ( m) Area = b h = 18.5 m = 2.5 m 6.0 m = 15.0 m 2 b) Perimeter = (2 3.4 cm) + (2 9.3 cm) Area = b h = 25.4 cm = 9.3 cm 3.0 cm = 27.9 cm 2 2. a) Area = (a + b) h 2 b) Area = (a + b) h 2 = (12 cm + 4 cm) 6.4 cm 2 = (5.0 cm cm) 6.5 cm 2 = 51.2 cm 2 = 35.8 cm 2 3. a) Area = (b h) 2 b) Area = (b h) 2 = (7.0 m 4.5 m) 2 = (8.5 cm 12.0 cm) 2 = 15.8 m 2 = 51.0 cm 2 c) Area = (b h) 2 = (9.0 cm 4.5 cm) 2 = 20.3 cm 2 4. a) Area of the parallelogram = b h = 9 cm 9 cm = 81 cm 2 b) Area of trapezoid = (a + b) h 2, where a = 12 cm and b = 12 (3 + 3) = 6 cm = (12 cm + 6 cm) 9 cm 2 = 81 cm 2 5. Area of the small square = b h Area of the one triangle = (b h) 2 = 2 cm 2 cm = (2 cm 2 cm) 2 = 4 cm 2 = 2 cm 2 Area of four triangles = 4 2 cm 2 = 8 cm 2 Area of the large square that is shaded = area of small square + area of four triangles = 4 cm cm 2 = 12 cm 2 6. a) Area of rectangle = l w Area of trapezoid = (a + b) h 2, where a = 2 m and b = 8 m = 6 m 12 m = (2 m + 8 m) 4 m 2 = 72 m 2 = 20 m 2 Total area of floor = 72 m m 2 = 92 m 2 I calculated the area of the rectangle and the area of the trapezoid. I then added them together to get the total area of the floor. b) Perimeter = 12 m + 6 m + 2 m + 5 m + 2 m + 5 m + 2 m + 6 m = 40 m Chapter 5 Task (Master) pp Answers will vary greatly depending on the Adventurepark design created. A sample design is as follows: A. triangles: amusement ride areas parallelograms: wave pool, restaurants, washroom trapezoids: extreme sports park, complex polygons: water park, restaurant and patio Attractions that will be included in my design: amusement rides, wave pool, water park, an extreme sports park, restaurant, and trees Copyright 2006 by Thomson Nelson Chapter 5 Answers 63

3 B. Restaurant (#1) Amusement Rides (#3) Patio Extreme Tree Wave Pool (#7) Sports Park (#2) Water Park (#6) Kid s Amusement Rides (#4) Tree Tree Washroom (#5) C. Shape (design) Perimeter formula Perimeter Area formula Area #1 P = a + b + c + d + e + f P = 40 cm A trapezoid = (a + b) h 2 Total area = A1 + A2 (complex polygon) P = 13 cm + 7 cm + 3 cm A1 = (13 cm + 7 cm) A1 = 30 cm cm + 3 cm + 7 cm 3 cm 2 A2 = 91 cm 2 A rectangle = l w Total area = 121 cm 2 A2 = 7 cm 13 cm #2 P = a + b + c + d + e + f P = 42 cm A trapezoid = (a + b) h 2 Total area = A1 + A2 (trapezoid) P = 4 cm + 7 cm + 10 cm A1 = (4 cm + 8 cm) A1 = 42 cm cm + 10 cm + 7 cm 7 cm 2 A2 = 60 cm 2 A2 = (4 cm + 8 cm) Total area = 102 cm 2 10 cm 2 #3 P = a + b + c P = 46 cm A triangle = (b h) 2 A = 102 cm 2 (triangle) P = 12 cm + 17 cm + 17 cm A = (12 cm 17 cm) 2 #4 P = a + b + c P = 38 cm A triangle = (b h) 2 A = 78 cm 2 (triangle) P = 13 cm + 12 cm + 13 cm A = (12 cm 13 cm) 2 #5 P = 2(a + b) P = 16 cm A = b h A = 12 cm 2 (parallelogram) P = 2(6 cm + 2 cm) A = 6 cm 2 cm #6 P = 2(a + b) P = 48 cm A rectangle = l w Total area = A1 + A2 + A3 (complex polygon) P = 2(15 cm + 9 cm) A1 = 15 cm 9 cm A1 = 135 cm 2 A trapezoid = (a + b) h 2 A2 = 30 cm 2 A2 = (15 cm + 5 cm) A3 = 25 cm 2 3 cm 2 Total area = 190 cm 2 A rectangle = l w A3 = 5 cm 5 cm #7 P = 2(a + b) P = 38 cm A = b h A = 100 cm 2 (parallelogram) P = 2(9 cm +10 cm) A = 10 cm 10 cm 64 Chapter 5: 2-D Measurement Copyright 2006 by Thomson Nelson

4 D. Name of design/shape Restaurant: complex polygon Extreme sports park: trapezoids Description of design/shape I calculated the area of the trapezoid ((a + b) h 2) and the area of the rectangle and added them together to get the total area of the restaurant. I calculated the areas of both trapezoid ((a + b) h 2) and added them together to get the total area of the sports park. Amusement rides: triangle I calculated the area of the triangle using the formula (b h) 2. Kid s amusement rides: triangle I calculated the area of the triangle using the formula (b h) 2. Washroom: parallelogram I calculated the area of the triangle using the formula b h. Water park: complex polygon I calculated the area of the two trapezoids ((a + b) h 2) and the area of the rectangle, and added them together to get the total area of the water park. Wave pool: parallelogram I calculated the area of the triangle using the formula b h. Answers to Chapter Project (continued from p. 8) G. H.The materials I will need for the walls, and the cost of those materials. Area covered Amount of Cost of Material Area to be covered by materials materials needed materials Wall paint Area = l w 1 can of paint 1 large can $38.95 = 2(5 m 2.5 m) + 2(4 m 2.5 m) covers 45 m 2 = 45 m 2 Stencil N/A N/A 1 stencil $14.95 Stencil paint 1 small can 1 small can $18.95 covers 12 m 2 Curtains Area = l w 1 m 2 $20.00 = 1 m 1 m = 1 m 2 L. Hardwood Area = l w Area of wood floor tiles Need $4.49 floor = 4 m 5 m = 0.3 m 0.3 m floor tiles = $ = 20 m 2 = 0.09 m 2 Hardwood Area = l w 20 m 2 8 pieces of trim 8 $9.95 floor trim = 4 m 5 m each 2.5 m long = $79.69 = 20 m 2 I. K. I will pull up carpet and replace it with hardwood flooring. Around the edge of the floor, I will put a trapezoid pattern in the wood. 5 m 4 m L. Refer to Table. M. I will use trim to place a chair rail on all walls around the room. N. Amount of trim needed is (2 5 m) + (2 4 m) = 18 m Area below trim = 18 m 1 m = 18 m 2 A small can of paint covers an area of 12 m 2. Therefore, the amount of paint required to paint a different colour below the chair rail is 2 small cans. O. The window is 1 m 1 m, the bedroom door is 2 m 2 m, and the closet door is 2 m 2 m. Copyright 2006 by Thomson Nelson Chapter 5 Answers 65

5 P. Area of wall with window = (5 m 2.5 m) (1 m 1 m) = 11.5 m 2 Total wall area (not including windows and doors) = Total wall area area of door area of closet door area of window = 45 m 2 (2 m 2 m) (2 m 2 m) (1 m 1 m) = 36 m 2 Q. I subtracted the area of the windows and doors from the total area of the walls. R. T. Students choose a partner and share their designs. U. The cost of the design includes all materials used, including paint, flooring. The cost of paint is determined by the area that must be painted. A large can of paint covers about 45 m 2. A small can of paint covers about 12 m 2. The design on the hardwood would be an additional cost to the total cost of the flooring. V. The most challenging part of the project was estimating how much money it would cost to decorate the room. W. Students will listen to their partner s presentation. Answers to Lesson 5.1, Checking (continued from p. 16) 6. a) For example, A height height B base height base C base b) For example, parallelogram A is 6 squares, parallelogram B is 12 squares, and parallelogram C is 6 squares. c) For example, Area of A = b h Area of B = b h Area of C = b h = 3 cm 2 cm = 6 cm 2 cm = 6 cm 1 cm = 6 cm 2 = 12 cm 2 = 6 cm 2 7. Area = b h Area = b h = 8.0 m 4.0 m = 5.0 m 6.4 m = 32.0 m 2 = 32.0 m 2 Answers to Lesson 5.2, Checking (continued from p. 20) 3. b) Area of triangle = (b h) 2 = (6 cm 4 cm) 2 6 cm = 24 cm cm = 12 cm 2 Area of parallelogram = (b h) = (6 cm 4 cm) = 24 cm 2 66 Chapter 5: 2-D Measurement Copyright 2006 by Thomson Nelson

6 c) 2 cm 8 cm Area of triangle = (b h) 2 Area of parallelogram = (b h) = (8 cm 2 cm) 2 = (8 cm 2 cm) = 16 cm 2 2 = 16 cm 2 = 8 cm 2 4. a) For example, b) For example, c) For example, d) For example, 5. A B C D Estimates: for example, triangle A is 2 cm 2, triangle B is 3.5 cm 2, triangle C is 2 cm 2, and triangle D is 2 cm 2. I predict that triangles A, C, and D have the same area. Area of triangle A = (b h) 2 Area of triangle B = (b h) 2 = (2 cm 2 cm) 2 = (3 cm 2.5 cm) 2 = 4 cm 2 2 = 7.5 cm 2 2 = 2 cm 2 = 3.75 cm 2 Area of triangle C = (b h) 2 Area of triangle D = (b h) 2 = (2 cm 2 cm) 2 = (1 cm 4 cm) 2 = 4 cm 2 2 = 4 cm 2 2 = 2 cm 2 = 2 cm 2 Copyright 2006 by Thomson Nelson Chapter 5 Answers 67

7 Answers to Lesson 5.2, Key Assessment of Learning Question (continued from p. 20) 7. (Application of Learning) a) Area = (b h) 2 b) Area = (b h) 2 = (3 cm 3 cm) 2 = (1.5 cm 2.0 cm) 2 = 9 cm 2 2 = 3 cm 2 2 = 4.5 cm 2 = 1.5 cm 2 Answers to Lesson 5.4, Learn About the Math (continued from p. 27) C. Area of triangle 1 = (b h) 2 Area of triangle 2 = (b h) 2 = (20 m 60 m) 2 = (40 m 60 m) 2 = 600 m 2 = 1200 m 2 Area of rectangle = l w = 40 m 60 m = 2400 m 2 D. Area of trapezoid = 600 m m m 2 = 4200 m 2 E. 100 m 40 m 60 m 40 m 100 m F. Area of the parallelogram = b h = 140 m 60 m = 8400 m 2 G. Area of the trapezoid = (b h) 2 = (140 m 60 m) 2 = 4200 m 2 Answer to Lesson 5.6, Key Assessment of Learning Question (continued from p. 38) b) The centre of the figure is located at the midpoint of the 8 cm length. Draw lines from the centre of the figure to create six congruent parallelograms. Each parallelogram has a base of 4.0 cm and a height of 36 mm, or 3.6 cm. Area of each parallelogram = b h = 4.0 cm 3.6 cm = 14.4 cm 2 Total area = area of parallelogram 6 = 14.4 cm 2 6 = 86.4 cm cm 4.0 cm 68 Chapter 5: 2-D Measurement Copyright 2006 by Thomson Nelson

Math 8 Notes Unit 8: Area and Perimeter

Math 8 Notes Unit 8: Area and Perimeter Syllabus Objective: (6.) The student will compute the perimeter and area of rectangles and parallelograms. Perimeter is defined as the distance around the outside