11-1 Practice 5.5 ft h parallelogram. 12 mm Find the perimeter and area and of each or triangle. to Round the Find the perimeter areaparallelogram of each parallelogram or Round triangle. to the 4 ft 2. nearest 3. 1) 3.5 m 2), if necessary. 40. tenth W(1, X(1, 6), Y(4, nearest tenth if necessary. 2. 41. A(-8, 0), B(-7, 4), C(-3, 3) 4m 3. 60˚ Areas and Triangles 3.5 of m Parallelograms ___________________________________ Hour _______ 2.4),parallelogram 3. Coordinate Geometry the -2) area of the Example 2 K(-7, D(0, E(2, 4), of F(6, G(6,2.0) Name -2), L(-7, 6), M(1, Find 6), N(7, 4.7or in.43. Find 1. the42. perimeter area each triangle. Round to the 1. 0),and 3. 8 cm 5.7 in. 10 in. 5m 8 cm 4.7 in. 10 in. 5m nearest tenth if necessary. 11-1 Areas5.7 of in. Triangles and Parallelograms (page 349) 10 mm 60˚ 1. 4. A(2, 0), B(7, 0), C(8, 4), D(3, 4) Worksheet 45˚ 45˚ 60˚ 11 m m of each 10 cm Find the5.8 area 5.8 m 11 m2. figure.6 in. Lesson 11-1 18 mm 45˚ 3. 10 cm 45˚ 6. I(2, 2), J(4, 2), K(2, -3), L(0, -3) 8 cm Find triangle 6isin. shaded, just find the area10of in. the shaded part. A=1/2bh 5 m the area of each Triangle. If the 44. 14 yd1. 4. d 11 m 4m 4m 25 ft 60˚ 4.45˚ 2. 5. 4. 45. 10 22 cm in. 26 in. 15 cm Example 3 21 cm 5. (page 350) 25 ftparallelogram with the45˚given vertices. ind the area of the try Find 45˚ cm the17area NAME 4. D(3, 4), D(3, 4) 4) C(8, 4), NAME 11-1 25 15 ft25cmcm 20 cm 20 in. Skills Practice 25 cm 3. 7. 200 m Find the value of h for each parallelogram. 6. 8. 9. 120 mh 12.8 ft PERIOD DATE 5. 0), 0), 5. E(-4, 0), F(-1, G(1, -3), H(-2, -3) 5. E(-4, 0), F(-1, G(1, -3), H(-2, -3) 6. 20 in. 6. 0),0), m 18.5 km 3), L(0, -3) -3) 7. M(-6, -1), N(-5, P(1, 0),0), Q(0, -1) (2,3.4-3), L(0, 7. M(-6, -1), N(-5, P(1, Q(0, -1) 17 cm 6. of the parallelogram with the given vertices. 17 cm 15 cm 46. 45˚ 5. DATE 14 12.8 ft 0.3 40 m 8 ft PERIOD 8 ft 60 m 8 10 The Greek mathematician Heron is most famous for this formula 11-1 History Skills Practice Areas ofancient Parallelograms and Triangles for the area of a triangle in terms of the lengths of its sides a, b, and c. enge 15 cm or each parallelogram. ach parallelogram. 25 cm 9 km 12 in. 20 in. 12 16 in. in. 12.8 ft 16 in. 8 ft 4 ft 46ftft 6 ft Find4. the of10. each 5. parallelogram or triangle.6.Round to the 9. perimeter and area10. 9. the area of each shaded triangle. Example 0.52 a)(s 2 12b)(s nearest tenth 0.5 4+ ft b + c) 6 ft in. A if=necessary. " s(s s 4= 12(aFind 13in. h2hc)16, where 30 cm 0.3 13 7. of aheight parallelogram its 350) base. thebase. area of the 0.3The height 8. is 5 feet more (page 7. The of a parallelogram is 5 than feet more thanIf its 1212 60˚ h 204 square 11. If the area of the 12. 1. 2. h parallelogram is feet, find its base and height. 20 cm parallelogram is 204area square of feet,each find its base and height. 4.5 yd Find the perimeter and parallelogram or triangle. Round 5.5 ftthe area 5.7 18 17 in. to find m 5 m Round your Use Heron’s Formula and a calculator of each triangle. 10 18 0.4 0.4 12 mm Areas of Parallelograms and Triangles h shaded 7. triangle. 49. a = 6 cm, b = 7 cm, 8. c = 11 cm 5.5ft,ft c = 11 ft 9. b = 10.2 50. a = 10 ft, Lesson 11-1 1. Skills Practice Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. parallelogram is 204 square feet, find its base and height. 60˚ 8. The18height of aheight parallelogram is three its17 base. Ifits the thearea The of9a in., parallelogram is three the of the parallelogram 13 in.times in.times mm8. 10 mm m 17 47. a = 8 in., b = c = 10 in. 48. a base. =area 15Ifofm, b4parallelogram = m,3 m c = 21 m 2. is 972 square inches, find its base and height. is 972 square inches, find its base and height. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 4m Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. nearest tenth ifthenecessary. 7. The height of ato parallelogram 5 feetDATE more than 4its the area of the ft base. IfPERIOD answer nearestis whole number. 7. Example ded 8. triangle. 12 mm Theof height of a parallelogram is three times its base. If the5area of14. theLandscaping parallelogramTaisha’s Bakery has a pla Areas Parallelograms and Triangles height of12. a parallelogram is 10 feet more 13.than its base. If the area of the ft parking lot. The four par (page 351) is 97251. square inches, find its Formula base and height. 4aft50 ft-by-31 a.square Use Heron’s to find the area of 4.5 yd 9. The base of a triangle is four times its height. If the area of the triangle is allelogram is 1200 feet, find its base and height. 12. 13. rimeter and area of each parallelogram or triangle. Round to the 6 yd 9. The base of a triangle is four times its height. If the area of the triangle is m spaces are congruent parallelograms, the 4.5242 yd square 15 in. millimeters, find its base and height. 26 in. the triangle at the right. 3. 4. 3 ft 6 yd 242 square millimeters, find its base and height. th if necessary. 9 in. 14 yd 60˚ is a rectangle, and the two unpav region mm 10 mm to part (a) by 3 in.ftusing the b.18Verify your answer 22 for 7.5 yd 9. The base of is a triangle times height. the area of the is flowers are congruent triangles. one half is of four its height. If the area Ifof the triangle is triangle 196 see square 1 2. its m base of 7aydtriangle7.5 12 Practice. in. area of the surface to be pav For more practice, Extra formula A = bh. 45˚ 45˚ yd a. Find the 242 square millimeters, find its 2 ftheight. 2 base and 5.52 ftft limeters, find its base and height. 10. FRAMING A rectangular poster measures 42 inches by 26 inches. A frame shop fittedshop fitted 1210. mmFRAMING A rectangular inches. A frame blem Solving the areas of the driving region 2 ft poster 2 ftmeasures 42 inches by 26 adding the poster with a half-inch mat border. 4 ft isha’s Bakery has a plan for with a half-inch the poster mat border. For moreFor practice, see Extra Practice. spaces. more practice,the seefour Extraparking Practice. Find the area ofparking each Parallelogram. A=bh lot.has The sarking Bakery a four plan for a. Find the area of the poster. 60˚ b. Describe another method for finding a. Find theposter area ofmeasures the poster. 10. Problem FRAMING A rectangular 42 inches by 26 inches. A frame shop fitted m Solving mm 10 mm eple and Solving Find the area of driving each parallelogram. uent parallelograms, the 5. 6. 3.4 m 18.5 km ng lot. The four parking 10. poster 11. 12. area of the surface to be paved. the with a half-inch mat border. b. Find the ofthe thearea mat of border. b.area Find the mat border. ngle, and the two unpaved areas 10 ft3.5 m 9 km 1. 2. 3. the driving eparallelograms, 13. c. Use your method 26 in.from part (b) to fin 4. marked a. Find the area of the poster. ice by Example ongruent triangles. Find the area of each parallelogram. c. Suppose the wall is marked where the poster will hang. The area includes 14 yd 15 cm c.12 Suppose the wall is marked where the poster will hang. the marked area includesanswers from the area of each parallelogram. 49)Find and the two unpaved areas cm area. Then compare 10 ft the poster and frame. Find the The an additional 12-inch space around total wall area of the surface to bearea paved by an additional 12-inch space around the poster and frame. Find the total wall area 4.7 in. b. Find the of the mat border. 22 in. 1. been marked for 2. 3. 5.7parts Example 1that has uent1. triangles. 3.5 m 50 the ft poster. your work. in. (a) and (b) to check 2. 3. 3.5 m that has been marked for the poster. eas of(page the driving region and 20 cm 15 cm 349) 12 cmwhere the poster will 7 yd e surface to be paved by is marked c. Suppose the wall hang. The marked area includes 26 m in. 15 cm 5.8 4. ng 50 4.7 in. 45˚ftaround 30 cm12 cm yd spaces.an additional 5.7 in. 6Geometry in.45˚ 12-inch space the poster and frame. Find the total wall area fther the7. driving region and 11 7 Glencoe 8. Standardized Test Prep 4.7 in. 60˚ method for finding the 20 cm 22 in. 5.7 in. that has been marked for the poster. paces. 5.8 m 20 cm 20 cm rface to be paved. 6 in. in. 45˚ 445˚ m of 5.8 m triangle17are method for finding Choice 52. The lengths of the sides a right 10 in., 24 in., and 26 in. hodMultiple from part (b) tothe find 6 in. What is the area of 15 thefttriangle? be paved. Chapter 11 Chapter 8 Glencoe Geometry nto compare answers from 11 8 Glencoe Geometry 4parallelogram m 2 the area 2 2 15. 10:57:11 AM 13. 14. B. Coordinate Geometry Find of120 the with the given6/1/09 vertices. erom 2 part in. C. 130 in. D. 156 in.2 A. 116 in. 31 ft (b)your to find (b) to check work. PDF Pass 13 in. 17 in. 49)5. 15 6. 4Find mft 3.4 m 18.5 km C 53.0), What is4), theD(3, area4) of $ABCD atofthe D mpare answers 4. A(2, 0),Coordinate B(7, C(8, 5. E(-4, 0), F(-1, 0), G(1, -3), -3) Geometry the area theright? parallelogram with theH(-2, given vertices. Example 2 from Lesson 7-1 Areas of Parallelograms and Triangles 351 Chapter 11 8 Glencoe Geometry 2 2 6. 18.5 G.31 64ft in. km F. 32 in. (page 349)work. o check your Lesson 7-1 Areas o 4. A(2, 0), B(7, 0), C(8, 4), D(3, 4) 5. E(-4, 0), F(-1, 0), G(1, -3), H(-2, -3) 6. I(2,Geometry 2), J(4, 2), H. K(2, -3), 7. M(-6, -1), N(-5, 0), P(1, 0), Q(0,8 -1) 2L(0, Coordinate Find the area-3) of I.the45.6 parallelogram with the given 001_025_CRMGEOC11_890520.indd 8 6/1/09 10:57:18 AM 91.2 in. in.2 in. 9 km vertices. 001_025_CRMGEOC11_890520.indd 8 6/1/09 11.3 in. Lesson 11-1 CISES Pass 9 feet km more than its base. If the area of 9. The height of 6. a parallelogram is 10 the0), Q(0, PDF I(2, 2), J(4, 2), K(2, -3), L(0, -3) 7. M(-6, -1), N(-5, 0), PDF P(1, -1) A for parallelogram 176 ft0), G(1, -3), H(-2, -3) A(2, B(7, 0), C(8, 4), D(3,parallelogram. 4) has 5. 0),of F(-1, is54. 1200 square feet, findadjacent itsE(-4, basesides and height. Find0),the value of h each e 3 4. parallelogram A 8 in. B and 312 ft. The altitude to the shorter side is 5_CRMGEOC11_890520.indd 8 50) Find the value of h for each parallelogram. Example 3 6. I(2,8.2), J(4, 2), K(2,290 -3), L(0, -3) 7.ofM(-6, -1), N(-5, is the area the parallelogram? 10. 0), P(1, 0), Q(0, -1) h ft. What2 9. 0.5 2 (page 350) B. 51,352 ft C. 54,912 ft2 h D. 55,202 ft2 A. 51,040 ft 13 10. 8.14 0.3 9. 12 square h m 10. The base of a triangle 0.5 of the triangle is 196 is one half 8. of its height.hIf the area 13 PDF Pass Pass 6/1/09 10:57:18 AM 11-1 Practice Areas ofAreas Parallelograms and Triangles ofParallelograms Parallelograms andTriangles Triangles 3. Areas of and of Parallelograms and Round Triangles e perimeter andAreas area of each parallelogram or triangle. to the 14 yd Find the perimeter andarea areaofofYou’ll each parallelogram triangle. Round the Find the area of eachand Parallelogram. need to use Special Right Triangles orRound Trig. A =to bhto Find the perimeter each parallelogram oror triangle. the tenth if necessary. Find the perimeter and area of each parallelogram or triangle. Round to the 7 yd nearest tenth necessary. nearest tenth ififnecessary. DATE PERIOD 45˚ 16. 17. 18. nearest tenth if necessary. 2. 1. 1. 1.55mm 5.5 ft 2.2. 2.8 4cm 8ftcm 12 mm 5m 60˚ 60˚ ams 60˚ 18 mmand 10Triangles mm 11 11mm 11 m 3. 3. 3. 8 cm 45˚ 45˚ 60˚ 45˚ 1010 cmcm 10 cm 5. arallelogram or triangle. Round to the 15 15cm cm 15 cm 22 in. 7. 60˚ 20 cm 35. Probability Ann drew these three figures on a grid. A fly 12.8 lands ft ftat random at a 12.8 45˚ 8 ft 8 ft 12.8 ft point on the grid. 8 ft 2020 in.in. 2525cm cm 25 cm 20 in. Lesson 11-1 17 174cm cm ft 17 cm 60˚ 45˚ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 35. 2. Probability Ann drew these three figures on a grid. A fly lands at random at a 4. 5.5. 6. 6. 4. point on 5.5 26 in. theft grid. 4.5. 6. 30 cm 14 4. yd .4 m ˚ 35. Probability Ann drew these three figures on a grid. A fly lands at random at a 20. 21. point on the grid. Lesson 11-1 19. 10 in. 10 in. 10 in. 3.4 45˚ 45˚m 45˚ 21. The height of a parallelogram is 5 feet more than its base. If the area of the parallelogram is 204 square feet, find its 6. base and height. 4 ft 6 ft 12 in. 18.5 km 16 in. 12 in. 16 in. 4 ft 6 ft 4 ft 6 ft 12 in. 16 in. a. Writing Is the fly more 9 km likely to land on one of the figures or on the blank 26 in. 4. a. Writinggrid? Is theExplain. fly more likely to land on one of the figures or on the blank 9. The height of a parallelogram is 10 feet m 22 in. parallelogram 1200 likely squareto feet, find it grid?b.Explain. Suppose you know the fly lands on one of the figures. Is the flyismore 7. height of a parallelogram is 5 feet more than its base. If the area of the 45˚ 7.7.The The height of a parallelogram is 5 feet more than its base. If the area of the 22. The height of a parallelogram is Is 3lands times its base. Ifof the area ofits thebase. parallelogram is 972 likely square find its base b. Suppose you know the fly on one the figures. Isone the fly tothe blank land one figure than on another? The height of aon parallelogram is 5fly feet more than Ifofthe area ofor the a. Writing the more likely toExplain. land on themore figures oninches, 30 cm parallelogram is 204 square feet, find its base and height. and height. parallelogram 204 square find base 8. land on oneisis figure than onfeet, another? Explain. parallelogram 204grid? square feet, findits its base and and height. height. Explain. 20 cm find its base and height. land on figure on another? Explain. Coordinate Geometry Find theone area of athan polygon with the givenmillimeters, vertices. 6. 18.5 km 36. A(3, 9), B(8, 9), C(2, -3), D(-3, -3) 37. E(1, 1), F(4, 5),of G(11, 5), H(8, 1) 8. height of aaparallelogram isisthree times itsitsbase. If If the area of the parallelogram 8.8.The The height of parallelogram three times base. the area the parallelogram 36. A(3, 9), B(8, 9), C(2, -3), D(-3, -3) 37. E(1, 1), F(4, 5), G(11, 5), H(8, 1) The height of a parallelogram is three times its base. If the area of the parallelogram 23. base ofinches, a triangle is fourits times its height. If the the area ofofthe is with 242 square millimeters, find its base and Coordinate Geometry Find area a triangle polygon the given vertices. 9 kmThe is square find base and height. 13 in. 17 in. isis972 972 find its height. 38.square M(-2,inches, -5), L(1, N(2,and -2)height. 972 square inches, find-5), itsbase base and height. 39. R(-7, 2), S(-3, -1), T(3, -1) 38. M(-2, -5), L(1, -2) 39.D(-3, R(-7, 2), S(-3, -1), T(3,5), -1) 36.-5), A(3, N(2, 9), B(8, 9), C(2, -3), -3) 37. E(1, 1), F(4, G(11, 5), H(8, 1) 40. W(1, 2), X(1, 6), Y(4, 1) 41. A(-8, 0), B(-7, 4), C(-3, 3) 38.Y(4, M(-2, -2) 0), B(-7, 39. R(-7, 2), S(-3, 40. W(1, 2), X(1, 6), 1) -5), L(1, -5), N(2, 41. A(-8, 4), C(-3, 3) -1), T(3, -1) eight of a parallelogram is 10 feet more than its base. If the area of the 9. base of aa0), triangle isis2), four times its 1) height. IfIfthe area ofof the triangle isC(-3, D(0, E(2, 4), F(6, 4), G(6, 0) 43. K(-7, -2), L(-7, 6), M(1, 6), 9.9. The base of triangle four times height. the area the triangle is 40. W(1, X(1, 6), Y(4, 41. A(-8, 0), B(-7, 4), 3) N(7, -2) 8.The lelogram is42. 1200 square feet, find its base andits height. 42. D(0, 0), E(2, 4), F(6, 4), G(6, 0) 43. K(-7, -2), L(-7, 6), M(1, 6), N(7, The base of a triangle is four times its height. If the area of the triangle is-2) 242 square millimeters, find its base and height. Find each area. You will have to divide the figure into triangles and parallelograms, then add the areas together. 242 find its base and height. 242square squaremillimeters, millimeters, base4), and 42. D(0, 0),find E(2, its 4), F(6, G(6,height. 0) 43. K(-7, -2), L(-7, 6), M(1, 6), N(7, -2) 17 in. Find each figure. 24.the 25. 26. Find areathe of area each of figure. ase of a triangle is one Find half the of its height. If the area of the triangle is 196 square area of each figure. Chapter46. 11 44. 45. m 25 ft 15 cm by46. 44.FRAMING 45. meters, find its base height. poster m shop200 25 ft 15 cm 42 inches 10. A and rectangular measures 26 inches. A 200 frame fitted 10. FRAMING AArectangular poster measures by A fitted 13 in. 17 in. 44. 45. 42 46. 200 m 21 cm ft 21 cm 15 cm 10.the FRAMING rectangular poster measures 42 inches inches by 26 26 inches. inches. A frame frame shop shop fitted poster with a half-inch25mat border. the poster with a half-inch mat border. 21 cm the poster with a half-inch mat border. 120 m 120 m 25 ft 25 ft a. Find the area of 25 theft poster. 120 m a.a. Find Findthe thearea areaofofthe theposter. poster. 001_025_CRMGEOC11_890520.indd 7 40 m 40 m t more than its base. If the area of the 40 m b. Find the area of the mat border. 60 m 25 ft 20 cm 60 m 25 ft 20 cm b.b.and Find the area of the mat border. its base height. 60 m 25 ft border. 20 cm Find the area of the mat c. Suppose the wall is marked where the poster will hang. The marked area includes c.c. Suppose the wall isisThe marked where the poster will hang. The area includes History The ancient Greek mathematician Heron isand most famous formarked this formula the wall marked where the poster willframe. hang. The marked area Challenge ngeC History ancient Greek mathematician Heron is most famous for this formula History The ancient Greek mathematician Heron is most famous for this formula anSuppose additional 12-inch space around the poster Find the total wall area an additional 12-inch space around the poster and frame. Find the total wall area an additional 12-inch space around the poster and frame. Find the total wall for the area of a triangle in terms of the lengths of its sides a, b, and c. for areafor ofisthe a196 triangle inof terms the lengths ofsides its sides andc.c. marked poster. height. Ifthat the area of the triangle square forhas the been area ofthe a triangle in terms theoflengths of its a, a, b,b,and that thathas hasbeen beenmarked markedfor forthe theposter. poster. 72c)a)(s Glencoe A2=b)(s "s(s2 21c) , where+ = (a + bGeometry A = "A s(s=2"a)(s , where c) 12+ 2(a +s b s(s 2 a)(s 2 b)(s 2 2 b)(s c)s ,= where = 12s (a b ++ c) c) Use and Heron’s Formula and a calculator find thetriangle. area of each triangle. Use Heron’s Formula a calculator to find the areatoof each Round yourRound your Use Heron’s Formula and a calculator to find the area of each triangle. Round your answer to the nearest whole number. answer to the nearest whole number. answer to the nearest whole number. 47. a = 8 in., b = 9 in., c = 10 in. 48. a = 15 m, b = 6/1/09 17 m,10:57:11 c =AM21 m Chapter PDF Pass 47. a 11 = 8 in., b = 9 in., c = 10 in. 48.8a = 15 m, b = 17 m, c = 21 m Glencoe Geometry Chapter 11 8 Glencoe Geometry Copyright©©Glencoe/McGraw-Hill, Glencoe/McGraw-Hill,aadivision divisionofofThe TheMcGraw-Hill McGraw-HillCompanies, Companies,Inc. Inc. Copyright Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. base triangle is onetohalf of its he b. Suppose Find you know the flyoflands on one of10. theThe figures. Is of thea fly more likely Coordinate Geometry the area 17 in. a polygon with the given vertices. 12 8 cm 8 cm 87° 87° Findprocess the area trianglewith using 6 SAS cm method. This canofbeeach generalized the the following formula: 6 in 140° 6 in 140° 6 cm T H E AREA FORM UL A FOR A T RI ANGL E A For a triangle with side lengths a, b, and c, and opposite angles of A, B, and C, the area is given by: b c Name___________________________________ 1 Area 2 ab sin C Date________________ Period____ C B a Exercise #2: Which of the following represents the exact area, in square inches,29.of an equilateral triangle 27. 28. r to the nearest tenth. whose sides have a length of 10 inches? 3) 2) (1) 50 2 8 yd 3)98° (3) 25 2 5 in 4) Dr. Neal, WKU 3 yd 4) 8 yd Scalene Triangles and Heron’s Formula 98° 140° 3 yd n 3.2 Area 6 in Name___________________________________ 3 3 Heron’s Formula gives the area a , b , and (4) c . 25 e has sides(2)of10length Then ng Heron's Formula Date________________ Period____ le to 4 in 96° 7 in 96 AL GEBRA 2 W I T H T RI GONOM ET RY , UNI T #9 ± T RI GONOM ET RI C APPL I CAT I ONS ± L ESSON #1 the area of each triangle using eM AT HHeron’s I NST RUCT I Formula. ON, RED H OOK , NY 12571, © 2009 theFind nearest tenth. Area s(s ! a)(s ! b)(s ! c) 3) - WS Section 3.2= Area 2) E Name___________________________________ 2 of each to -the nearest tenth. 14 ft Mr.triangle Butera Area using Heron's 16 ft 30. 31. Date________________ Period____ Name___________________________________ Formula Date________________ Period____ 2) sides that measure 6 yd and 5) A triangletowith Find the area of each triangle the two nearest 6 fttenth. D E 2 yd with an included angle of 10°. F 1)4 inof the following triangle: 2) he area 6) A triangle with two sides that measure 6 m a 8 m with an included angle of 137°. Z 6 ft that 5) A triangle with twoE sides D measure 6 yd and 14 ft 2 yd16with an included angle of 10°. ft Z 4) 6 in X n 4 in 14 Y 12 4 in X 7 in 7 in D 6 ft 1 Formula a - Area using Heron's PreCalc (M453) - WS Area where s = Section (a + b3.2 + c) 6) A triangle with two s 8 m with an included 14 ft 16 ft F 96° 7 in 20triangle with two sides that measure 5 cm and 7) A 8 cm with an included angle of 39°. 32. F 8) A triangle with two sides that measure 8 ft an 7 ft with an included angle of 30°. (12 + 14 + 20) = 23. Then4)the area is 7) A triangle with two sides that measure 5 cm and A 8 cm with an included angle of 39°. 16 mi 0)(23 ! 14)(23 ! 12) = 16 km m 5 in 5 in 23 ! 3 ! 9 ! 11 = C 12 mi 6831 9 mi ! 82.65 sq. units. 4) B A 6) A triangle with two ©5 i2t0q1522 vK MuMtxah 4SSoifKtNwx a5rSe6 TLOLisides Cr.a 9 5AtlVlU rr0i3gthat ghHtNsH Trme2svmeasure efrrvSe1dD.z P JM0azdeeg ewJirt6 zhF kI6nm tfXionkihtand 8eM aG0eroLm3eptaroyL.o 3) 8 m with an included angle of 137°. 16 mi 4) F D 14 km C 12 mi 11 km Wo A 16 mi B ©5 i2t0q1522 vKMuMtxah 4SSoifKtNwxa5rSe6 TLOLiCr.a 9 5AtlVlU rr0i3gghHtNsH Trme2svefrrvSe1dD.z P JM0azdeeg ewJirtzhF kI6ntfXionkiht8eM aG0ero9Lmmi 3eptaroyL.o C E -1- 9 mi 16 km D 8) A triangle with two s 7 ft with an included 12 mi B -1-

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