Lesson 15.1 Skills Practice

Transcription

1 Lesson 15.1 Skills Practice Name Date Customary to Whom? Customary Measurement Vocabulary Match each definition to its corresponding term. 1. to change a measurement to an equivalent measurement in different units a. standard units of measure 2. units used by everyone in a certain area b. measurement 3. the magnitude of a quantity specified with a number and a unit c. convert Problem Set Determine an approximate measure in customary units for each item. 1. the height of a stamp 2. the capacity of a jug of milk The height of a stamp is about one inch. 3. the weight of a loaf of bread 4. the weight of a slice of bread 5. the capacity of a fruit juice box 6. the average length of an adult shoe Chapter 15 Skills Practice 843

2 Lesson 15.1 Skills Practice page 2 Choose the appropriate customary unit of measure to use when measuring each of the following. 7. the length of a bicycle 8. the capacity of a bottle of glue The length of a bicycle would be best measured in inches or feet. 9. the weight of a tennis ball 10. the height of a tree 11. the distance of a marathon race 12. the capacity of a swimming pool Choose the most appropriate measurement for each of the following. 13. the capacity of a bottle of water a. 8 oz b. 16 fl oz c. 4 lb d. 14 gal b. 16 fl oz 14. the weight of a blue whale a. 500 yd b. 2 t c. 300,000 lb d. 56 c 15. the length of a car a. 13 ft b lb c. 26 in. d. 45 qt 844 Chapter 15 Skills Practice

3 Lesson 15.1 Skills Practice page 3 Name Date 16. the capacity of a car s gas tank a. 20 fl oz b. 5 mi c. 3 t d. 16 gal 17. the average weight of a newborn baby a. 8 lb b. 9 oz c. 7 yd d. 6 gal 18. the length of a cat s tail a. 15 mi b. 12 in. c. 5 c d. 8 fl oz Complete each model. Multiply to determine each measurement conversion. 19. How many inches are in 2 feet? 2 ft? in. 1 ft 12 in. 1 ft 2 ft ( 12 in. 1 ft ) 5 24 in. There are 24 inches in 2 feet. 20. How many cups are in 3 pints?? c 1 pt 3 pt Chapter 15 Skills Practice 845

4 Lesson 15.1 Skills Practice page How many ounces are in 2 pounds? 2 lb? oz 1 lb 22. How many yards are in 12 feet? 12 ft 1 yd? ft 23. How many quarts are in 16 cups? 16 c 1 qt? c 846 Chapter 15 Skills Practice

5 Lesson 15.1 Skills Practice page 5 Name Date 24. How many pounds are in 48 ounces? 48 oz 1 lb? oz Multiply to determine each measurement conversion. 25. How many feet are in 3 miles? 3 mi ( 5280 ft 1 mi ) 5 15,840 ft There are 15,840 feet in 3 miles. 26. How many pounds are in 5 tons? 27. How many fluid ounces are in 8 cups? 28. How many yards are in 504 inches? 29. How many pounds are in 480 ounces? 30. How many gallons are in 200 quarts? Chapter 15 Skills Practice 847

6 Lesson 15.1 Skills Practice page How many ounces are in 1 ton? 32. How many yards are in 2 miles? 33. How many inches are in 1 mile? 34. How many fluid ounces are in 2 pints? 35. How many pints are in 3 gallons? 36. How many fluid ounces are in 4 quarts? 848 Chapter 15 Skills Practice

7 Lesson 15.2 Skills Practice Name Date It s All Based on Powers of 10! Metric Measurement Vocabulary Choose the term from the box that best completes each statement. gram meter prefix liter 1. The standard unit of length in the metric system is the. 2. The standard unit of capacity is the. 3. The standard unit of mass is the. 4. A is a group of letters attached to the beginning of a word which changes the meaning of the word. Problem Set Choose the appropriate metric unit of measure to use when measuring each of the following. 1. the width of a roadway 2. the mass of a horse The width of a roadway would be best measured in meters. 3. the capacity of a fish tank 4. the length of a road between two cities 5. the mass of a penny 6. the capacity of a pond Chapter 15 Skills Practice 849

8 Lesson 15.2 Skills Practice page 2 Choose the most appropriate measurement for each of the following. 7. the mass of a tiger a. 30 mg b. 75 kl c. 95 kg d. 45 cm c. 95 kg 8. the length of a basketball court a. 29 m b. 85 ml c. 30 mm d. 12 g 9. the capacity of a mug a. 300 L b. 250 ml c. 400 mg d. 300 km 10. the mass of a bowling ball a. 6 mg b. 9 L c. 5 m d. 7 kg 11. the length of a pencil a. 20 km b. 16 mg c. 18 cm d. 14 ml 12. the capacity of a bucket a. 9 kl b. 6 L c. 8 g d. 10 mm Complete each sentence with the appropriate number or unit of measure. 13. A meter is 100 centimeters. 14. One thousand grams is A milligram is of a gram. 16. A kiloliter is liters. 17. A is 1 of a meter. 18. A liter is Chapter 15 Skills Practice

9 Lesson 15.2 Skills Practice page 3 Name Date Use the metric system chart to determine each measurement conversion dam 5 50 m km(1000) hm(100) dam(10) m(1) dm(0.1) cm(0.01) mm(0.001) km 5 dam km(1000) hm(100) dam(10) m(1) dm(0.1) cm(0.01) mm(0.001) dm 5 37 cm km(1000) hm(100) dam(10) m(1) dm(0.1) cm(0.01) mm(0.001) hm m km(1000) hm(100) dam(10) m(1) dm(0.1) cm (0.01) mm(0.001) Chapter 15 Skills Practice 851

10 Lesson 15.2 Skills Practice page dam 5 mm km(1000) hm(100) dam(10) m(1) dm(0.1) cm(0.01) mm(0.001) km 5 dm km(1000) hm(100) dam(10) m(1) dm(0.1) cm(0.01) mm(0.001) Multiply to determine each measurement conversion. 25. How many centimeters is 3.4 kilometers? 3.4 km ( 1000 m 1 km ) m 3400 m ( 100 cm 1 m ) 5 340,000 cm 26. How many meters is 350 millimeters? There are 340,000 centimeters in 3.4 kilometers. 27. How many milligrams is 12.9 kilograms? 28. How many grams is 25 milligrams? 29. How many liters is 3.75 kiloliters? 30. How many kiloliters is 269 milliliters? 852 Chapter 15 Skills Practice

11 Lesson 16.1 Skills Practice Name Date The Language of Geometry Sketching, Drawing, Naming, and Sorting Basic Geometric Figures Vocabulary Sketch an example of each geometric figure. 1. triangle 2. quadrilateral 3. square 4. rectangle 5. polygon 6. scalene triangle 7. equilateral triangle 8. regular polygon 9. irregular polygon 10. pentagon 11. equiangular triangle 12. hexagon 13. isosceles triangle 14. nonagon 15. kite 16. obtuse triangle 17. acute triangle 18. octagon 19. rhombus 20. trapezoid 21. right triangle 22. heptagon 23. parallelogram 24. decagon 25. isosceles trapezoid Chapter 16 Skills Practice 865

12 Lesson 16.1 Skills Practice page 2 Write the term that best completes each statement. 26. When you a geometric figure, the figure is created with the use of tools such as a ruler, a straightedge, a compass, or a protractor. 27. A(n) is a tool used to create arcs or circles. 28. In a quadrilateral, are sides that do not share a common endpoint. 29. A(n) is a ruler with no numbers. 30. When you a geometric figure, the figure is created using only a compass and a straightedge. 31. A(n) can be used to approximate the measure of an angle. 32. In a polygon, are sides that share a common endpoint. 33. When you a geometric figure, the figure is created without the use of tools. 866 Chapter 16 Skills Practice

13 Lesson 16.1 Skills Practice page 3 Name Date Problem Set Name each polygon and list its sides and angles. 1. T F 2. Q T M D Z W Sample answer. Name of Polygon: quadrilateral MTFD R B Sides: MT, TF, FD, and DM Angles: /M(or /DMT ), /T (or /MTF ), /F (or /TFD), and /D(or FDM ) Name of Polygon: Sides: Angles: 3. H 4. K Y G M X S C Name of Polygon: Sides: Angles: Name of Polygon: Sides: Angles: Chapter 16 Skills Practice 867

14 Lesson 16.1 Skills Practice page 4 5. P 6. W T X M Z E X R N B A J T Name of Polygon: Sides: Angles: W Name of Polygon: Sides: Angles: 868 Chapter 16 Skills Practice

15 Lesson 16.1 Skills Practice page 5 Name Date Sort the given polygons into the appropriate categories. A B C D E F G H J K 7. Regular polygons: C, F, H, and K Irregular polygons: A, B, D, E, G, and J 8. Polygons with at least one right angle: Polygons with no right angles: 9. Polygons with at least one pair of congruent sides: Polygons with no congruent sides: 10. Polygons with at least one obtuse angle: Polygons with no obtuse angles: 11. Polygons with at least one pair of opposite sides parallel: Polygons with no opposite sides parallel: 12. Polygons with at least one acute angle: Polygons with no acute angles: Chapter 16 Skills Practice 869

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17 Lesson 16.2 Skills Practice Name Date Pulling a One-Eighty! Triangle Sum, Exterior Angle, and Exterior Angle Inequality Theorems Vocabulary Write the term that best completes each statement. 1. The states that the measure of an exterior angle of a triangle is greater than the measure of either of the remote interior angles of the triangle. 2. The states that the sum of the measures of the interior angles of a triangle is The states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles of the triangle. 4. The are the two angles that are non-adjacent to the specified exterior angle. Problem Set Determine the measure of the unknown angle in each triangle. 1. B 2. P Q A C m/b ( ) 5 65 R Chapter 16 Skills Practice 871

18 Lesson 16.2 Skills Practice page 2 3. K 4. G 35 M 28 L F E 5. W 6. T X V 35 U Y List the side lengths from shortest to longest for each diagram. 7. B a 48 C 8. b S c 21 r t A T 60 s 54 R m/c ( ) The shortest side of a triangle is opposite the smallest angle. So, the side lengths from shortest to longest are a, b, c. 872 Chapter 16 Skills Practice

19 Lesson 16.2 Skills Practice page 3 Name Date 9. L 28 m k 118 K l M 10. Y x Z 42 y 84 X z 11. X a 27 W Y b 12. c e d Z B u r t A s D v C Chapter 16 Skills Practice 873

20 Lesson 16.2 Skills Practice page 4 Identify the interior angles, the exterior angle, and the remote interior angles of each triangle. 13. W X Y 14. T U Z R S Interior angles: /XYZ, /YZX, /ZXY Exterior angle: /WXZ Remote interior angles: /XYZ, /YZX 15. F 16. B E G H C A D 17. L J K M 18. Q P R S 874 Chapter 16 Skills Practice

21 Lesson 16.2 Skills Practice page 5 Name Date Solve for x in each diagram. 19. J 130 F G x 99 H K 20. R x 132 T U 140 S V m/gfh m/ghk 5 m/gfh 1 m/fgh x 49 5 x 21. H x I 2x K J U (x + 8) R T V S Chapter 16 Skills Practice 875

22 Lesson 16.2 Skills Practice page K 24. M 132 J (2x + 4) G 90 F 112 L N D (3x + 2) (2x + 18) E Compare the angles in each triangle and determine the unknown information. 25. T 26. R Q P Q R S S m/ QRT.m/RST m/pqr m/qrs m/ RTS, m/qrt m/qsr, m/ 876 Chapter 16 Skills Practice

23 Lesson 16.2 Skills Practice page 7 Name Date 27. T U 28. J W V F G H m/tuv m/uwv m/ m/ghj m/wvu m/tuv m/gjh m/fgj 29. K L M 30. A B N C D m/lmn m/kln m/abc m/bcd m/lnm m/kln m/bac, m/ Chapter 16 Skills Practice 877

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25 Lesson 16.3 Skills Practice Name Date Triangle Construction I Constructing Triangles Problem Set Determine whether each combination of given sides and/or angles determines a unique triangle. 1. You are given three angles. No. 2. You are given three sides. 3. You are given two sides and the included angle. 4. You are given two angles and a side not specified. 5. You are given two angles. 6. You are given two sides. Chapter 16 Skills Practice 879

26 Lesson 16.3 Skills Practice page 2 Construct each triangle using the given sides and/or angles. 7. Construct PQR using the three line segments shown. P Q Q R P R Q P R 8. Construct UVW using the three line segments shown. W V U W U V 880 Chapter 16 Skills Practice

27 Lesson 16.3 Skills Practice page 3 Name Date 9. Construct DEF using the three line segments shown. D D E E F F 10. Construct MNP using the three line segments shown. M N M N P P Chapter 16 Skills Practice 881

28 Lesson 16.3 Skills Practice page Construct HJK using the three line segments shown. H K J H J K 12. Construct ABC using the two line segments and included angle shown. A B A C A 882 Chapter 16 Skills Practice

29 Lesson 16.3 Skills Practice page 5 Name Date 13. Construct PQR using the two line segments and included angle shown. P Q P R P 14. Construct DEF using the two line segments and included angle shown. D E E F E Chapter 16 Skills Practice 883

30 Lesson 16.3 Skills Practice page Construct KMN using the two line segments and included angle shown. K M N M M 16. Construct WXZ using the two line segments and included angle shown. W W X Z W 884 Chapter 16 Skills Practice

31 Lesson 16.4 Skills Practice Name Date Triangle Construction II Congruent Figures and Constructing Congruent Triangles Vocabulary Define each term in your own words. 1. geometric figures 2. congruent geometric figures 3. corresponding sides 4. corresponding angles 5. included angle 6. included side Chapter 16 Skills Practice 885

32 Lesson 16.4 Skills Practice page 2 Problem Set Use measuring tools to determine whether the given figures are congruent. If the figures are congruent, then identify and list the corresponding sides and angles. If the figures are not congruent, explain why they are not. 1. A B E F D C H G The figures are congruent. AB > FE, BC > EH, CD > HG, AD > FG, /A > /F, /B > /E, /C > /H, and /D > /G 2. J K P Q N M S R 886 Chapter 16 Skills Practice

33 Lesson 16.4 Skills Practice page 3 Name Date 3. B C W X A D Z Y 4. A D E B C F Chapter 16 Skills Practice 887

34 Lesson 16.4 Skills Practice page 4 5. M G J N H K 6. Q T S P R U 888 Chapter 16 Skills Practice

35 Lesson 16.4 Skills Practice page 5 Name Date Construct each triangle using the given sides and/or angles. 7. Three sides are given. a b c a b c 8. Three sides are given. d e f Chapter 16 Skills Practice 889

36 Lesson 16.4 Skills Practice page 6 9. Three sides are given. h g k 10. Two sides and the included angle are given. b a 890 Chapter 16 Skills Practice

37 Lesson 16.4 Skills Practice page 7 Name Date 11. Two sides and the included angle are given. c d 12. Two sides and the included angle are given. e f Chapter 16 Skills Practice 891

38 Lesson 16.4 Skills Practice page Two angles and the included side are given. g 892 Chapter 16 Skills Practice

39 Lesson 16.4 Skills Practice page 9 Name Date 14. Two angles and the included side are given. h Use the congruence symbol to show the corresponding sides and angles that are congruent based on each congruence statement. 15. nmat > njef MA > JE, AT > EF, MT > JF, /M > /J, /A > /E, /T > /F 16. nlmn > nghj 17. ncat > ndog 19. npqr > nxyz 18. nabc > nktv 20. ndef > nrst Chapter 16 Skills Practice 893

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41 Lesson 16.5 Skills Practice Name Date Pasta Anyone? Triangle Inequality Theorem Vocabulary Use the given figure to complete the statement. 1. According to the Triangle Inequality Theorem, 1. AC. B A C Problem Set Without measuring the angles, list the angles of each triangle in order from least to greatest measure. 1. G 9 in. 2. Y 8 in. F 11 in. H 4.7 cm 3.6 cm X 2.1 cm W The smallest angle of a triangle is opposite the shortest side. So, the angles from least to greatest are /H, /F, /G. Chapter 16 Skills Practice 895

42 Lesson 16.5 Skills Practice page 2 3. Q 4. T 12 in S 8 ft 4 ft 9 in 15 in P 6.43 ft R U 5. F 6. K 4.6 yd 9.2 yd 5.8 m 4.2 m E 6 yd G M 5.2 m L Determine whether it is possible to form a triangle using segments with the given measurements. Explain your reasoning in., 2.9 in., 5 in ft, 9 ft, 11 ft Yes. Because , and 5.9 is greater than Chapter 16 Skills Practice

43 Lesson 16.5 Skills Practice page 3 Name Date 9. 4 m, 5.1 m, 12.5 m cm, 8.1 cm, 9.8 cm yd, 5 yd, 21 yd km, 6.3 km, 7.5 km mm, 300 mm, 190 mm in., 11 in., 8.2 in cm, 12 cm, 17 cm ft, 8 ft, 8 ft Chapter 16 Skills Practice 897

44 Lesson 16.5 Skills Practice page 4 Write an inequality that expresses the possible lengths of the unknown side of the given triangle. 17. What could be the length of AB? 18. What could be the length of DE? A D 10 m 6 cm B 8 m C F 9 cm E AB, AC 1 BC AB, 10 m 1 8 m AB, 18 m AC, AB 1 BC AC 2 BC, AB 10 m 2 8 m, AB 2 m, AB 2 m, AB, 18 m 898 Chapter 16 Skills Practice

45 Lesson 16.5 Skills Practice page 5 Name Date 19. What could be the length of HI? I 20. What could be the length of JL? J 20 in. 12 ft H 14 in. G K 7 ft L Chapter 16 Skills Practice 899

46 Lesson 16.5 Skills Practice page What could be the length of MN? 22. What could be the length of QR? M P N 11 cm O 3 cm 9 mm 13 mm R Q 900 Chapter 16 Skills Practice

47 Lesson 17.2 Skills Practice Name Date Weaving a Rug Area and Perimeter of Rectangles and Squares Problem Set Calculate the perimeter of each given rectangle. Each square on the grid represents a square that is 1 foot long and 1 foot wide Perimeter 5 2(12) 1 2(8) feet Chapter 17 Skills Practice 911

48 Lesson 17.2 Skills Practice page Calculate the perimeter of each given rectangle in in. 2 in. 5 in. P 5 2(5) 1 2(3) in m 2 m 8 m 12 m 912 Chapter 17 Skills Practice

49 Lesson 17.2 Skills Practice page 3 Name Date ft 9.5 m 9.5 m 8 ft Calculate the area of each given rectangle. Each grid square is 1 foot long and 1 foot wide Area 5 6(13) 5 78 square feet Chapter 17 Skills Practice 913

50 Lesson 17.2 Skills Practice page Calculate the area of each given rectangle cm cm 11 cm A 5 11(3) 5 33 cm 2 7 cm m 1.75 m 11.2 m 2.3 m 914 Chapter 17 Skills Practice

51 Lesson 17.2 Skills Practice page 5 Name Date ft in. 14 ft 12 in. In each rectangle, the length, width, or area is unknown. Calculate the value of the unknown measure Area: 12 ft 2 Area: 35 ft 2 Length: 4 ft A 5 lw w 3 5 w Length: 7 ft The width is 3 feet yd 5 yd 2 yd 13 yd Chapter 17 Skills Practice 915

52 Lesson 17.2 Skills Practice page Area: 30 in. 2 Width: 4 in. Area: 65 m 2 Width: 5 m Calculate the missing measures using the given measure for each square. 31. Side length: 6 feet 32. Side length: 18 centimeters Area: 36 square feet Area: Perimeter: 24 feet Perimeter: 33. Side length: 34. Side length: Area: 16 square inches Area: Perimeter: Perimeter: 36 meters 35. Side Length: 5.5 inches 36. Side Length: Area: Area: 400 square meters Perimeter: Perimeter: Calculate the perimeter and area of a rectangle or square whose dimensions are double the dimensions of each given rectangle or square. 37. A rectangle with a perimeter of 14 meters and an area of 10 square meters The rectangle whose dimensions are doubled will have the following perimeter and area. Perimeter 5 2 (14) 5 28 meters Area 5 4 (10) 5 40 square meters 916 Chapter 17 Skills Practice

53 Lesson 17.2 Skills Practice page 7 Name Date 38. A rectangle with a perimeter of 30 feet and an area of 54 square feet 39. A square with a perimeter of 60 meters and an area of 225 square meters 40. A square with a perimeter of 14 inches and an area of square inches 41. A rectangle with a perimeter of 42 meters and an area of 20 square meters Chapter 17 Skills Practice 917

54 Lesson 17.2 Skills Practice page A square with a perimeter of 72 feet and an area of 324 square feet Calculate the area of each composite figure m ft 8 m 8 m 8 m 6 ft 2 ft 8 m 4 ft A 5 24 (8) 1 8 (8) m in ft 14 in. 8 in. 14 in. 5 ft 9 ft 6 in. 5 in. 5 in. 6 in. 10 ft 6 ft 6 ft 18 ft 918 Chapter 17 Skills Practice

55 Lesson 17.2 Skills Practice page 9 Name Date m m 7 m 16 m 4 m 5 m 4 m 5 m 7 m 16 m 7 m 14 m ft m 7 ft 8 ft 7 ft 6 ft 4 m 3.5 m 3.5 m 8 m 6 m 6 m 4 m 6 m 6 m 6 ft 20 ft Chapter 17 Skills Practice 919

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57 Lesson 17.3 Skills Practice Name Date Boundary Lines Area of Parallelograms and Triangles Vocabulary Define each term in your own words. 1. altitude of a parallelogram 2. height of a parallelogram 3. altitude of a triangle 4. height of a triangle Chapter 17 Skills Practice 921

58 Lesson 17.3 Skills Practice page 2 Problem Set Calculate the area of each given parallelogram. Each square on the grid represents a square that is 1 centimeter long and 1 centimeter wide Area 5 6(9) 5 54 square centimeters Chapter 17 Skills Practice

59 Lesson 17.3 Skills Practice page 3 Name Date Calculate the area of each parallelogram mi 8. 6 mi 8 mi 11 mi A 5 8(4) 5 32 mi yd 16 yd 14 yd 7 yd In each given parallelogram, the base, height, or area is unknown. Calculate the value of the unknown measure in. 4.5 ft 8.5 in. A 5 8.5(8) 5 68 in ft Chapter 17 Skills Practice 923

60 Lesson 17.3 Skills Practice page Area: 36 m 2 Area: 63 m 2 18 m 9 m 15. Area: 96 ft Area: 286 ft 2 12 ft 22 ft Area: 138 m 2 15 ft 12 ft 9.2 m 924 Chapter 17 Skills Practice

61 Lesson 17.3 Skills Practice page 5 Name Date The base of each triangle is labeled. Draw a segment that represents the height of the triangle b h b b b 23. b 24. b Chapter 17 Skills Practice 925

62 Lesson 17.3 Skills Practice page 6 Calculate the area of each given triangle. Each square on the grid represents a square that is 1 foot long and 1 foot wide Area 5 1 (12)(8) 5 48 square feet Chapter 17 Skills Practice

63 Lesson 17.3 Skills Practice page 7 Name Date Calculate the area of each given triangle in ft 8 in. 7 ft A 5 1 (6)(8) 5 1 (48) 5 24 in m 4 m 20 mm 11 mm in 18 in 12 m 14 m Chapter 17 Skills Practice 927

64 Lesson 17.3 Skills Practice page 8 In each given triangle, the base, height, or area is unknown. Calculate the value of the unknown measure. 37. Area: 30 sq. m ft A bh (15)h h 4 5 h 15 m 3 ft The height of the triangle is 4 meters in. 3 yd Area: 35 sq. in. Area: 6 sq. yd 41. Area: 88 sq ft ft 6 in. Area: 31.5 sq in. 928 Chapter 17 Skills Practice

65 Lesson 17.3 Skills Practice page 9 Name Date Calculate the area of each shaded region. 43. The figure is composed of 2 triangles. 15 m 9 m 20 m The area of the large triangle is: The area of the small triangle is: A 5 1 bh 2 A bh 5 1 (20)(15) (20)(9) m m 2 The shaded area m The figure is composed of a parallelogram and a triangle. 7 yd 10 yd 5 yd 2 yd Chapter 17 Skills Practice 929

66 Lesson 17.3 Skills Practice page The figure is composed of 2 triangles. 16 m 6 m 14 m 46. The figure is composed of a parallelogram and a triangle. 8 ft 3 ft 9 ft 930 Chapter 17 Skills Practice

67 Lesson 17.3 Skills Practice page 11 Name Date 47. The figure is composed of 2 triangles. 6 in. 8 in. 3 in. 12 in. 48. The figure is composed of 2 parallelograms and 1 triangle. 22 m 9 m 9 m 3 m Chapter 17 Skills Practice 931

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69 Lesson 17.4 Skills Practice Name Date The Keystone Effect Area of Trapezoids Vocabulary Explain how the set of terms are related. 1. legs of a trapezoid and bases of a trapezoid 2. altitude of a trapezoid and height of a trapezoid Problem Set Calculate the area of each trapezoid. Each square on the grid represents a square that is 1 inch long and 1 inch wide A 5 1 (8 1 4) (12)(5) 5 30 The area of the trapezoid is 30 square inches. Chapter 17 Skills Practice 933

70 Lesson 17.4 Skills Practice page Calculate the area of each trapezoid with the given dimensions, where h represents the height, b 1 represents the length of a base, and b 2 represents the length of the other base. 7. h 5 2, b 1 5 4, b h 5 6, b 1 5 5, b A 5 1 (4 1 3) (7)(2) 5 7 The area is 7 square units. 9. h 5 3, b , b h 5 5, b 1 5 9, b Chapter 17 Skills Practice

71 Lesson 17.4 Skills Practice page 3 Name Date 11. h 5 1 2, b , b h 5 4, b , b In each given trapezoid, the length of one base, the height, or the area is unknown. Calculate the value of the unknown measure feet 3 feet centimeters Area: 8 square centimeters 2 centimeters 2 feet A 5 1 (2 1 4) (6)(3) 5 9 The trapezoid has an area of 9 square feet. 15. Area: 5 square feet 3 feet 1 feet yards Area: 25 square yards 8 yards Chapter 17 Skills Practice 935

72 Lesson 17.4 Skills Practice page millimeters yards 4 millimeters Area: 70 square yards 5 yards Area: 14 square millimeters 19. Area: 13.5 square inches feet 3 inches 3 inches 5 feet 22 feet meters 5 yards 2 yards 8 yards 7 meters Area: 98 square meters 936 Chapter 17 Skills Practice

73 Lesson 17.4 Skills Practice page 5 Name Date Use the given information to answer each question. 23. The side of a staircase has the shape of a trapezoid with the dimensions shown in the diagram. You want to paint this side of the staircase. How many square feet will you need to cover with paint? 13 feet 11 feet 26 feet A (b 1 b )h 1 2 A 5 1 ( )11 2 A You will need to cover square feet with paint. 24. Yvonne cut a picture into the shape of a trapezoid to place into her scrapbook. The picture is shown. What is the area of the picture? 5 in. 7 in. 4 in. Chapter 17 Skills Practice 937

74 Lesson 17.4 Skills Practice page A mosaic on a CD cover is in the shape of an isosceles trapezoid with the dimensions shown in the diagram. The artist needs to tell the production company the area of the mosaic. How many square inches is the mosaic? 4 inches 4 inches 3 inches 26. The planning committee submitted a plan to the town architect to revitalize the town square. Their plan includes a new flagpole with a concrete base in the shape of a trapezoid. The base of the trapezoid and its dimensions are shown. What is the area of the base proposed by the planning committee? 5 feet 4 feet 7 feet 938 Chapter 17 Skills Practice

75 Lesson 17.4 Skills Practice page 7 Name Date 27. An aeronautical engineering student has painted a rocket-shaped design on her T-shirt. The design is composed of a triangle, a rectangle, and a trapezoid. How many square inches is the design? 4 in. 9 in. 3 in. 4 in. 6 in. Chapter 17 Skills Practice 939

76 Lesson 17.4 Skills Practice page An advertising company has designed its new logo. The logo is composed of two trapezoids. What is the area of the shaded region? 25 cm 8 cm 10 cm 12 cm 14 cm 940 Chapter 17 Skills Practice

77 Lesson 17.5 Skills Practice Name Date Go Fly a Kite Area of Rhombi and Kites Problem Set Calculate the area of each given rhombus or kite. Each square on the grid represents a square that is 1 foot long and 1 foot wide. 1. The polygon is a rhombus. 2. The polygon is a rhombus. A 5 bh 5 10 (8) 5 80 The area of the rhombus is 80 square feet. Chapter 17 Skills Practice 941

78 Lesson 17.5 Skills Practice page 2 3. The polygon is a rhombus. 4. The polygon is a kite. 942 Chapter 17 Skills Practice

79 Lesson 17.5 Skills Practice page 3 Name Date 5. The polygon is a kite. 6. The polygon is a kite. Chapter 17 Skills Practice 943

80 Lesson 17.5 Skills Practice page 4 Calculate the area of each given rhombus or kite. 7. The polygon is a rhombus. 15 in. 8. The polygon is a rhombus. 13 in. 7 m 8.5 m A 5 bh 5 15 (13) The area of the rhombus is 195 square inches. 9. The polygon is a rhombus. 12 yd 11 yd 944 Chapter 17 Skills Practice

81 Lesson 17.5 Skills Practice page 5 Name Date 10. In the given kite, AE 5 6 ft, CE 5 6 ft, BE 5 9 ft, and DE 5 15 ft. B A E C D 11. In the given kite, JK 5 3 meters, FK 5 7 meters, GK 5 12 meters, and HK 5 7 meters. F J K G H Chapter 17 Skills Practice 945

82 Lesson 17.5 Skills Practice page In the given kite, SZ 5 WZ 5 10 yards, TZ 5 12 yards, and RZ 5 32 yards. S R Z T W Calculate the area of each shaded region. 13. The figure is composed of 2 congruent rhombi. 20 ft 16 ft The area of 1 rhombus is: A 5 bh 5 20 (16) square feet The area of the figure is 2(320) square feet. 946 Chapter 17 Skills Practice

83 Lesson 17.5 Skills Practice page 7 Name Date 14. The figure is composed of a kite and a square. Given: AG 5 7 meters, BG 5 FG 5 8 meters, DG meters, and CE 5 9 meters. B C A G D E F Chapter 17 Skills Practice 947

84 Lesson 17.5 Skills Practice page The figure is composed of a trapezoid and a rhombus. 10 in. 8.5 in. 11 in. 24 in. 16. The figure is composed of 2 kites. Given: MR 5 RS 5 5 feet, ST 5 PT 5 10 feet, and NS 5 QS 5 12 feet. N M R S T P Q 948 Chapter 17 Skills Practice

85 Lesson 17.5 Skills Practice page 9 Name Date 17. The figure is composed of a square and a kite. Given: AE 5 9 inches, BE 5 DE 5 7 inches, and CE 5 15 inches. A B E D C Chapter 17 Skills Practice 949

86 Lesson 17.5 Skills Practice page The figure is composed of 2 congruent triangles and a rhombus. 4 in. 4 in. 5 in. 4 in. 950 Chapter 17 Skills Practice

87 Lesson 17.6 Skills Practice Name Date Street Signs Area of Regular Polygons Vocabulary Draw an example of each given term. 1. congruent polygons 2. apothem Problem Set Determine whether each polygon is a regular polygon The polygon is not a regular polygon. Chapter 17 Skills Practice 951

88 Lesson 17.6 Skills Practice page cm 5 cm cm cm 5 cm cm 4. 4 inches inches 4 inches inches 5. 3 ft ft ft 3 ft ft Draw an apothem of each given figure Chapter 17 Skills Practice

89 Lesson 17.6 Skills Practice page 3 Name Date Write a formula for the area of each regular polygon. State the area in terms of an apothem a of the polygon. 13. regular octagon with side h A 5 ( 1 2 ha ) ha 14. regular hexagon with side c 15. regular nonagon with side b 16. regular decagon with side d 17. regular pentagon with side length g 18. regular heptagon with side length t Calculate the area of each regular polygon cm cm A (8)(6.3)(6) A The area is square centimeters. 12 ft 8.3 ft Chapter 17 Skills Practice 953

90 Lesson 17.6 Skills Practice page yd 20 km 24.1 km 10.4 yd in in. 4.3 in. 7.5 in m 2 m 1 m 6 m Use the given information to calculate the area of each regular polygon. 27. A regular decagon has a side length of 26 yards and an apothem length of 40 yards. What is the area of the regular decagon? A (26)(40)(10) The area of the regular decagon is 5200 square yards. 954 Chapter 17 Skills Practice

91 Lesson 17.6 Skills Practice page 5 Name Date 28. A regular 15-gon has a side length of 10 feet and an apothem length of 23.5 feet. What is the area of the regular 15-gon? 29. A regular 12-gon has a side length of 11 meters and an apothem length of 20.5 meters. What is the area of the regular 12-gon? 30. A regular octagon has a perimeter of 36 millimeters and an apothem length of 5.4 millimeters. What is the area of the regular octagon? 31. A regular pentagon has a perimeter of 625 centimeters and an apothem length of 86 centimeters. What is the area of the regular pentagon? 32. A regular 20-gon has a perimeter of 1000 inches and an apothem length of inches. What is the area of the regular 20-gon? Chapter 17 Skills Practice 955

92 Lesson 17.6 Skills Practice page 6 Calculate the area of each shaded region. 33. The figure is composed of a regular pentagon and a square. 13 in. 20 in. 9 in. The area of the square is: The area of the pentagon is: A 5 s 2 A 5 ( 1 2 la ) n 5 (20) (13)(9)(5) square inches square inches The area of the shaded region is square inches. 34. The figure is composed of a regular hexagon and a square. 10 ft 11 ft 8.7 ft 956 Chapter 17 Skills Practice

93 Lesson 17.6 Skills Practice page 7 Name Date 35. The figure is composed of a regular pentagon and 2 congruent trapezoids. 10 cm 14 cm 13.3 cm 9.7 cm 19 cm 36. The figure is half of a regular octagon. 12 in in. Chapter 17 Skills Practice 957

94 Lesson 17.6 Skills Practice page The figure is composed of 2 regular pentagons. 10 m 15 m 6.9 m 10.3 m 38. The figure is composed of 4 congruent regular hexagons. 22 ft 19 ft 958 Chapter 17 Skills Practice

95 Lesson 17.7 Skills Practice Name Date Backyard Barbecue, Anyone? Volume of Rectangular Prisms Problem Set Calculate the volume of each rectangular prism in. 8 in. 2 in cm 14 cm 1.5 cm V 5 (8)? (2)? (5) V 5 80 in m 8 m 13 m 5 m 2 m 3.5 m 5. 4 in. 4 in. 4 in ft 21 ft 6 ft Chapter 17 Skills Practice 959

96 Lesson 17.7 Skills Practice page 2 Describe how you would separate each solid to calculate the volume Separate the solid into two rectangular prisms one prism is the bottom of the L, and the other prism is the top of the L Chapter 17 Skills Practice

97 Lesson 17.7 Skills Practice page 3 Name Date Calculate the volume of each solid formed by the rectangular prisms ft ft 2 ft 5 m 4 m 1 ft 1 ft V 5 top prism 1 bottom prism V 5 (1)(1)(1) 1 (4)(1)(1) 6 m 1 m 1 m V V 5 5 ft 3 Chapter 17 Skills Practice 961

98 Lesson 17.7 Skills Practice page cm 2 cm yd 2 yd 2 cm 2 cm 6 cm 6 cm 2 yd 4 yd 2 cm 1 cm 1 cm 6 yd 1 yd ft 2 ft mm 1 mm 12 ft 19 mm 2 ft 12 mm 9 ft 1 ft 1 mm 15 mm 962 Chapter 17 Skills Practice

99 Lesson 17.7 Skills Practice page 5 Name Date Determine the volume for each problem. 19. A storage box with a square base has a side length of 2 feet and a height of 2 1 feet. What is the 2 volume of the storage box? V 5 2(2) ( ) 5 4 ( 5 2 ) 5 10 The volume of the storage box is 10 cubic feet. 20. Your uncle and aunt bought new bedroom furniture including a dresser. The rectangular dresser is 5 feet tall, 3 1 feet wide, and 2 feet long. What is the volume of this new dresser? A carpenter is building a new table. Each of the four legs is a rectangular prism with a height of 3 feet, a width of 0.5 foot, and a length of 0.5 foot. What is the total volume of wood that the carpenter used to make the table legs? 22. A square stained glass window is created for a kitchen. The window has a side length of feet, and a width of 0.08 foot. What is the volume of the square window? Chapter 17 Skills Practice 963

100 Lesson 17.7 Skills Practice page Susan bought a new ottoman for her living room. It opens so she can store items inside. The height of the ottoman is 1 1 feet, the width is 2 feet, and the length is 2 1 feet. What is the total 2 4 volume of the ottoman? 24. Bryce is installing new gutters around the outside of his backyard shed. Each gutter is 10 feet long, 1 foot high, and 1 foot wide. What is the total volume of the four gutters Bryce is installing on 4 3 his shed? 964 Chapter 17 Skills Practice