Lesson 13.1 Skills Practice Name________________________________________________________ Date _________________________ The Language of Geometry Sketching, Drawing, Naming, and Sorting Basic Geometric Figures Vocabulary © 2011 Carnegie Learning 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 13 Skills Practice • 719 Lesson 13.1 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, 29. A(n) are sides that do not share a common endpoint. 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, 33. When you are sides that share a common endpoint. a geometric figure, the figure is created without the use of © 2011 Carnegie Learning tools. 720 • Chapter 13 Skills Practice Lesson 13.1 Skills Practice page 3 Name________________________________________________________ Date _________________________ Problem Set Name each polygon and list its sides and angles. 1. F 2. Q T T M Z D Sample answer. R Name of Polygon: quadrilateral MTFD Sides: MT, TF, FD, and DM Angles: /M (or /DMT ), /T (or /MTF ), /F (or /TFD), and /D (or FDM ) 3. W Name of Polygon: Sides: Angles: 4. H B K Y G S © 2011 Carnegie Learning M Name of Polygon: Sides: Angles: C X Name of Polygon: Sides: Angles: Chapter 13 Skills Practice • 721 Lesson 13.1 5. Skills Practice page 4 6. P W T Z X R T Name of Polygon: Sides: Angles: N X M E B A J W Name of Polygon: Sides: Angles: © 2011 Carnegie Learning 722 • Chapter 13 Skills Practice Lesson 13.1 Skills Practice page 5 Name________________________________________________________ Date _________________________ Sort the given polygons into the appropriate categories. A C B F E D G J H 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: © 2011 Carnegie Learning 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 13 Skills Practice • 723 © 2011 Carnegie Learning 724 • Chapter 13 Skills Practice Lesson 13.2 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. 2. 1. Perimeter 5 2(12) 1 2(8) 5 24 1 16 5 40 feet 4. © 2011 Carnegie Learning 3. Chapter 13 Skills Practice • 725 Lesson 13.2 Skills Practice 5. page 2 6. Calculate the perimeter of each given rectangle. 8. 7. 2 in. 3 in. 9 in. 5 in. P 5 2(5) 1 2(3) 5 10 1 6 5 16 in. 9. 10. 12 m 2m 8m 726 • Chapter 13 Skills Practice © 2011 Carnegie Learning 4m Lesson 13.2 Skills Practice page 3 Name_________________________________________________________ Date__________________________ 11. 12. 4.5 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. 13. 14. 16. © 2011 Carnegie Learning Area 5 6(13) 5 78 square feet 15. Chapter 13 Skills Practice • 727 Lesson 13.2 Skills Practice 17. page 4 18. Calculate the area of each given rectangle. 19. 3 cm 20. 4 cm 11 cm 7 cm A 5 11(3) 5 33 cm 2 21. 22. 2.5 m 11.2 m 2.3 m 728 • Chapter 13 Skills Practice © 2011 Carnegie Learning 1.75 m Lesson 13.2 Skills Practice page 5 Name_________________________________________________________ Date__________________________ 23. 14 ft 24. 12 in. 14 ft 12 in. In each rectangle, the length, width, or area is unknown. Calculate the value of the unknown measure. 25. 26. Area: 12 ft2 Area: 35 ft2 Length: 4 ft Length: 7 ft A 5 lw 12 5 4w 35w The width is 3 feet. 27. 28. 5 yd © 2011 Carnegie Learning 6 yd 2 yd 13 yd Chapter 13 Skills Practice • 729 Lesson 13.2 Skills Practice 29. page 6 30. Area: 30 in.2 Area: 65 m2 Width: 4 in. Width: 5 m Calculate the missing measures using the given measure for each square. 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 730 • Chapter 13 Skills Practice © 2011 Carnegie Learning 31. Side length: 6 feet Lesson 13.2 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 © 2011 Carnegie Learning 40. A square with a perimeter of 14 inches and an area of 12.25 square inches 41. A rectangle with a perimeter of 42 meters and an area of 20 square meters Chapter 13 Skills Practice • 731 Lesson 13.2 Skills Practice page 8 42. A square with a perimeter of 72 feet and an area of 324 square feet Calculate the area of each composite figure. 44. 8m 43. 11 ft 2 ft 8m 8m 6 ft 8m 8m 4 ft A 5 24 (8) 1 8 (8) 5 192 1 64 5 256 m2 46. 5 in. 8 ft 5 ft 8 in. 14 in. 9 ft 14 in. 6 in. 6 in. 10 ft 6 ft 5 in. 5 in. 732 • Chapter 13 Skills Practice 6 ft 18 ft © 2011 Carnegie Learning 45. Lesson 13.2 Skills Practice page 9 Name________________________________________________________ Date _________________________ 47. 48. 5m 7m 4m 7m 7m 5m 7m 16 m 14 m 4m 5m 16 m 49. 50. 20 ft 7 ft 7 ft 6m 6 ft 3.5 m 4m 8 ft 6m 8m 6m 6m 3.5 m 4m 6m 6 ft © 2011 Carnegie Learning 20 ft Chapter 13 Skills Practice • 733 © 2011 Carnegie Learning 734 • Chapter 13 Skills Practice Lesson 13.3 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 © 2011 Carnegie Learning 4. height of a triangle Chapter 13 Skills Practice • 735 Lesson 13.3 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. 2. 1. Area 5 6(9) 5 54 square centimeters 4. 5. 6. © 2011 Carnegie Learning 3. 736 • Chapter 13 Skills Practice Lesson 13.3 Skills Practice page 3 Name________________________________________________________ Date _________________________ Calculate the area of each parallelogram. 7. 8. 4 mi 6 mi 8 mi 11 mi A 5 8(4) 5 32 mi2 9. 10. 16 yd 32 yd 7 yd 14 yd In each given parallelogram, the base, height, or area is unknown. Calculate the value of the unknown measure. 12. © 2011 Carnegie Learning 11. 4.5 ft 8 in. 20 ft 8.5 in. A 5 8.5(8) 5 68 in.2 Chapter 13 Skills Practice • 737 Lesson 13.3 Skills Practice 13. page 4 14. Area: 36 m2 18 m Area: 63 m2 9m 15. 16. Area: 96 ft2 Area: 286 ft2 12 ft 22 ft 18. Area: 138 m2 12 ft 15 ft 738 • Chapter 13 Skills Practice 9.2 m © 2011 Carnegie Learning 17. Lesson 13.3 Skills Practice page 5 Name________________________________________________________ Date _________________________ The base of each triangle is labeled. Draw a segment that represents the height of the triangle. 19. 20. b h b 21. 22. b © 2011 Carnegie Learning b 23. b 24. b Chapter 13 Skills Practice • 739 Lesson 13.3 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. 26. 25. 1(12)(8) 5 48 square feet Area 5 __ 2 28. 29. 30. © 2011 Carnegie Learning 27. 740 • Chapter 13 Skills Practice Lesson 13.3 Skills Practice page 7 Name________________________________________________________ Date _________________________ Calculate the area of each given triangle. 31. 6 in. 32. 7 ft 8 in. 7 ft 1(6)(8) 5 __ 1(48) 5 24 in.2 A 5 __ 2 2 33. 34. 4.5 m 4m 20 mm 11 mm © 2011 Carnegie Learning 35. 36. 7.5 in 12 m 18 in 14 m Chapter 13 Skills Practice • 741 Lesson 13.3 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 38. 2 ft 15 m 3 ft 1 bh A 5 __ 2 1 (15)h 30 5 __ 2 60 5 15h 45h The height of the triangle is 4 meters. 39. 40. 3 yd 10 in. Area: 6 sq. yd 41. 42. Area: 88 sq ft 8 ft 742 • Chapter 13 Skills Practice 6 in. Area: 31.5 sq in. © 2011 Carnegie Learning Area: 35 sq. in. Lesson 13.3 Skills Practice page 9 Name________________________________________________________ Date _________________________ Calculate the area of each shaded region. 43. The figure is composed of 2 triangles. 15 m 9m 20 m The area of the large triangle is: The area of the small triangle is: 1 bh A 5 __ 2 1 (20)(15) 5 __ 2 5 150 m2 1 bh A 5 __ 2 1 __ 5 (20)(9) 2 5 90 m2 The shaded area 5 150 2 90 5 60 m2 44. The figure is composed of a parallelogram and a triangle. 7 yd © 2011 Carnegie Learning 10 yd 5 yd 2 yd Chapter 13 Skills Practice • 743 Lesson 13.3 Skills Practice page 10 45. The figure is composed of 2 triangles. 6m 16 m 14 m 46. The figure is composed of a parallelogram and a triangle. 3 ft 9 ft 744 • Chapter 13 Skills Practice © 2011 Carnegie Learning 8 ft Lesson 13.3 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 © 2011 Carnegie Learning 9m 9m 3m Chapter 13 Skills Practice • 745 © 2011 Carnegie Learning 746 • Chapter 13 Skills Practice Lesson 13.4 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 given trapezoid. Each square on the grid represents a square that is 1 inch long and 1 inch wide. 2. © 2011 Carnegie Learning 1. 1(8 1 4) 5 A 5 __ 2 1(12)(5) 5 __ 2 5 30 The area of the trapezoid is 30 square inches. Chapter 13 Skills Practice • 747 Lesson 13.4 Skills Practice page 2 3. 4. 5. 6. Calculate the area of each trapezoid with the given dimensions, where h represents the height, b1 represents the length of a base, and b2 represents the length of the other base. 8. h 5 6, b1 5 5, b2 5 3 1 (4 1 3)2 5 __ 1 (7)(2) 5 7 A 5 __ 2 2 The area is 7 square units. 9. h 5 3, b1 5 11, b2 5 7 748 • Chapter 13 Skills Practice 10. h 5 5, b1 5 9, b2 5 1 © 2011 Carnegie Learning 7. h 5 2, b1 5 4, b2 5 3 Lesson 13.4 Skills Practice page 3 Name________________________________________________________ Date _________________________ 1, b 5 10, b 5 14 11. h 5 __ 2 2 1 2 , b 5 __ 4 12. h 5 4, b1 5 __ 3 2 3 In each given trapezoid, the length of one base, the height, or the area is unknown. Calculate the value of the unknown measure. 13. 4 feet 14. 3 centimeters Area: 8 square centimeters 2 centimeters 3 feet 2 feet 1(2 1 4)3 5 __ 1(6)(3) 5 9 A 5 __ 2 2 The trapezoid has an area of 9 square feet. Area: 5 square feet 15. 16. 5 yards Area: 25 square yards 3 feet 1 feet © 2011 Carnegie Learning 8 yards Chapter 13 Skills Practice • 749 Lesson 13.4 17. Skills Practice 2 millimeters page 4 18. 15 yards 4 millimeters Area: 70 square yards 5 yards Area: 14 square millimeters 19. Area: 13.5 square inches 20. 13 feet 3 inches 5 feet 3 inches 22 feet 22. 21. 7 meters 5 yards 8 yards Area: 98 square meters © 2011 Carnegie Learning 2 yards 13 meters 750 • Chapter 13 Skills Practice Lesson 13.4 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 1(b 1 b )h A 5 __ 2 2 1 1 __ A 5 (26 1 13)11 2 A 5 214.5 You will need to cover 214.5 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. 4 in. © 2011 Carnegie Learning 7 in. Chapter 13 Skills Practice • 751 Lesson 13.4 Skills Practice page 6 25. 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? 4 feet 7 feet © 2011 Carnegie Learning 5 feet 752 • Chapter 13 Skills Practice Lesson 13.4 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. © 2011 Carnegie Learning 6 in. Chapter 13 Skills Practice • 753 Lesson 13.4 Skills Practice page 8 28. 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 10 cm 8 cm 12 cm © 2011 Carnegie Learning 14 cm 754 • Chapter 13 Skills Practice Lesson 13.5 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 © 2011 Carnegie Learning The area of the rhombus is 80 square feet. Chapter 13 Skills Practice • 755 Lesson 13.5 Skills Practice 4. The polygon is a kite. © 2011 Carnegie Learning 3. The polygon is a rhombus. page 2 756 • Chapter 13 Skills Practice Lesson 13.5 Skills Practice page 3 Name________________________________________________________ Date _________________________ 6. The polygon is a kite. © 2011 Carnegie Learning 5. The polygon is a kite. Chapter 13 Skills Practice • 757 Lesson 13.5 Skills Practice page 4 Calculate the area of each given rhombus or kite. 7. The polygon is a rhombus. 8. The polygon is a rhombus. 15 in. 7m 13 in. 8.5 m A 5 bh 5 15 (13) 5 195 The area of the rhombus is 195 square inches. 9. The polygon is a rhombus. 12 yd © 2011 Carnegie Learning 11 yd 758 • Chapter 13 Skills Practice Lesson 13.5 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 E A C D 11. In the given kite, JK 5 3 meters, FK 5 7 meters, GK 5 12 meters, and HK 5 7 meters. © 2011 Carnegie Learning F K J G H Chapter 13 Skills Practice • 759 Lesson 13.5 Skills Practice page 6 12. In the given kite, SZ 5 WZ 5 10 yards, TZ 5 12 yards, and RZ 5 32 yards. S Z R T W Calculate the area of each shaded region. 13. The figure is composed of 2 congruent rhombi. 20 ft The area of 1 rhombus is: A 5 bh 5 20 (16) 5 320 square feet The area of the figure is 2(320) 5 640 square feet. 760 • Chapter 13 Skills Practice © 2011 Carnegie Learning 16 ft Lesson 13.5 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 5 13.5 meters, and CE 5 9 meters. B C G A D E © 2011 Carnegie Learning F Chapter 13 Skills Practice • 761 Lesson 13.5 Skills Practice page 8 15. 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 R S T Q 762 • Chapter 13 Skills Practice P © 2011 Carnegie Learning M Lesson 13.5 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 E B D © 2011 Carnegie Learning C Chapter 13 Skills Practice • 763 Lesson 13.5 Skills Practice page 10 18. The figure is composed of 2 congruent triangles and a rhombus. 4 in. 5 in. 4 in. © 2011 Carnegie Learning 4 in. 764 • Chapter 13 Skills Practice Lesson 13.6 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 © 2011 Carnegie Learning Determine whether each polygon is a regular polygon. 2. 1. The polygon is not a regular polygon. Chapter 13 Skills Practice • 765 Lesson 13.6 Skills Practice 3. 5 cm 120° 120° 5. 3 ft 4 inches 110° 5 cm 120° 100° 6. 135° 135° 135° 135° 100° 3 ft 110° 70° 7 inches 3 ft 3 ft 4 inches 70° 5 cm 120° 5 cm 110° 4 inches 120° 5 cm 120° 4. 5 cm 120° page 2 135° 110° 135° 135° 3 ft 135° 7. 8. 9. 10. 11. 766 • Chapter 13 Skills Practice 12. © 2011 Carnegie Learning Draw an apothem of each given figure. Lesson 13.6 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 1 ha 8 5 4 ha A 5 __ 2 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. 19. 20. 8 cm 12 ft © 2011 Carnegie Learning 6.3 cm 8.3 ft 1(8)(6.3)(6) A 5 __ 2 A 5 151.2 The area is 151.2 square centimeters. Chapter 13 Skills Practice • 767 Lesson 13.6 Skills Practice 21. page 4 22. 10 yd 20 km 24.1 km 10.4 yd 24. 23. 4 in. 15 in. 7.5 in. 4.3 in. 26. 25. 12 m 2m 6m 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? 1 (26)(40)(10) A 5 __ 2 5 5200 The area of the regular decagon is 5200 square yards. 768 • Chapter 13 Skills Practice © 2011 Carnegie Learning 1m Lesson 13.6 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 © 2011 Carnegie Learning 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 157.8 inches. What is the area of the regular 20-gon? Chapter 13 Skills Practice • 769 Lesson 13.6 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 s2 1 la n A 5 __ 2 1 __ 5 (13)(9)(5) 2 5 292.50 square inches ( ) 5 (20)2 5 400 square inches The area of the shaded region is 400 2 292.50 5 107.50 square inches. 34. The figure is composed of a regular hexagon and a square. 10 ft 11 ft © 2011 Carnegie Learning 8.7 ft 770 • Chapter 13 Skills Practice Lesson 13.6 Skills Practice page 7 Name________________________________________________________ Date _________________________ 35. The figure is composed of a regular pentagon and 2 congruent trapezoids. 14 cm 10 cm 13.3 cm 9.7 cm 19 cm 36. The figure is half of a regular octagon. 12 in. © 2011 Carnegie Learning 14.5 in. Chapter 13 Skills Practice • 771 Lesson 13.6 Skills Practice page 8 37. The figure is composed of 2 regular pentagons. 15 m 10 m 6.9 m 10.3 m 38. The figure is composed of 4 congruent regular hexagons. 22 ft © 2011 Carnegie Learning 19 ft 772 • Chapter 13 Skills Practice

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