7th Grade Math. Determining if a Triangle is Possible. Slide 2 / 180. Slide 1 / 180. Slide 4 / 180. Slide 3 / 180. Slide 5 / 180.

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Adrian Clarke
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1 Side 1 / 180 Side 2 / 180 New Jersey Ceter for Teachig ad Learig Progressive Matheatics Iitiative This ateria is ade freey avaiabe at ad is iteded for the o-coercia use of studets ad teachers. These aterias ay ot be used for ay coercia purpose without the writte perissio of the owers. NJCTL aitais its website for the coveiece of teachers who wish to ake their work avaiabe to other teachers, participate i a virtua professioa earig couity, ad/or provide access to course aterias to parets, studets ad others. 7th Grade Math 2D Geoetry Cick to go to website: Side 3 / 180 Tabe of Cotets Deteriig if a Triage is Possibe Specia Pairs of Ages Perieter & Circuferece Area of Rectages Area of Paraeogras Area of Triages Area of Trapezoids Area of Circes Mixed Review Area of Irreguar Figures Area of Shaded Regios Cick o a topic to go to that sectio Side 4 / 180 Deteriig if a Triage is Possibe Retur to Tabe of Cotets Coo Core: 7.G.2, 7.G.4-6, 7.EE.3 Side 5 / 180 How ay differet acute triages ca you draw? How ay differet right scaee triages ca you draw? Reca that triages ca be cassified accordig to their side egths ad the easure of their ages. Sides: Scaee - o sides are cogruet Isoscees - two sides are cogruet Equiatera - a three sides are cogruet Ages: Acute - a three ages are acute Right - cotais oe right age Obtuse - cotais oe obtuse age Side 6 / 180 There is aother property that appies to triages: The su of the egths of ay two sides of a triage is greater tha the egth of the third side. What does this ea? If you take the three sides of a triage ad add the i pairs, the su is greater tha (ot equa to) the third side. If that is ot true, the it is ot possibe to costruct a triage with the give side egths.

2 Side 7 / 180 Side 8 / 180 Exape: Exape: Deterie if sides of egth 5 c, 8 c ad 12 c ca for a triage? Deterie if sides of egth 3 ft, 4 ft ad 9 ft ca for a triage? Test a three pairs to see if the su is greater: > > > 5 13 > > 8 20 > 5 Test a three pairs to see if the su is greater: > > > 3 7 > 9 12 > 4 13 > 3, it is possibe to costruct a triage with sides of egths 5 c, 8 c ad 12 c., it is ot possibe to costruct a triage with sides of egths 3 ft, 4 ft ad 9 ft. Side 9 / 180 Side 10 / 180 Try These: Deterie if triages ca be fored with the foowig side egths: 1 Deterie if sides of egth 5, 14 ad 19 ca for a triage. Be prepared to show your work! 1. 4 c, 7 c, 10 c 2. 24, 20, > > > > > > 24 YES YES 3. 7 ft, 9 ft, 16 ft 4. 9 i, 13 i, 24 i = < > > > > 9 NO NO Side 11 / 180 Side 12 / Deterie if sides of egth 6 i, 9 i ad 14 i ca for a triage. Be prepared to show your work! 3 Deterie if sides of egth 5 yd, 13 yd ad 21 yd ca for a triage. Be prepared to show your work!

3 Side 13 / 180 Side 14 / Deterie if sides of egth 3 ft, 8 ft ad 15 ft ca for a triage. Be prepared to show your work! 5 Deterie if sides of egth 5 i, 5 i ad 9 i ca for a triage. Be prepared to show your work! Side 15 / 180 Side 16 / A triage coud have which of the foowig sets of ages? 7 A triage coud have which of the foowig sets of ages? A A B B C D C D Side 17 / 180 Side 18 / 180 Exape: Exape: Predict the egth of the third side of a triage with sides of egth 12 ft ad 16 ft. Side 1 = 12 ft Side 2 = 16 ft The 3rd side ust be ess tha: > 3rd side 28 ft > 3rd side The 3rd side ust be greater tha: rd side > 16 3rd side > 4 The 3rd side ust be greater tha 4 ft ad ess tha 28 ft. Predict the egth of the third side of a triage with sides of egth 9 c ad 15 c. Side 1 = 9 c Side 2 = 15 c The 3rd side ust be ess tha: > 3rd side 24 c > 3rd side The 3rd side ust be greater tha: 9 + 3rd side > 15 3rd side > 6 The 3rd side ust be greater tha 6 c ad ess tha 24 c.

4 Side 19 / 180 Try These: Predict the egth of the third side of a triage whose kow sides are egths: 1. 13, i, 19 i > Side > Side 3 33 > Side 3 26 > Side Side 3 > Side 3 > 19 Side 3 > 7 Side 3 > 12 7 < side 3 < < side 3 < 26 Side 20 / 180 Try These: Predict the egth of the third side of a triage whose kow sides are egths: 3. 4 ft, 11 ft c, 34 c > Side > Side 3 15 > Side 3 57 > Side Side 3 > Side 3 > 34 Side 3 > 7 Side 3 > 11 7 < side 3 < < side 3 < 57 Side 21 / Predict the ower iit of the egth of the third side of a triage whose kow sides are egths 6 ad 12. Side 22 / Predict the upper iit of the egth of the third side of a triage whose kow sides are egths 6 ad 12. Side 23 / Predict the ower iit of the egth of the third side of a triage whose kow sides are egths 9 i ad 17 i. Side 24 / Predict the upper iit of the egth of the third side of a triage whose kow sides are egths 9 i ad 17 i.

5 Side 25 / Predict the ower iit of the egth of the third side of a triage whose kow sides are egths 15 ft ad 43 ft. Side 26 / Predict the upper iit of the egth of the third side of a triage whose kow sides are egths 15 ft ad 43 ft. Side 27 / 180 Side 28 / 180 Cogruet Ages have the sae age easureet. Specia Pairs of Ages Retur to Tabe of Cotets Side 29 / 180 Side 30 / Are the two ages cogruet? 15 Are the two ages cogruet ages? 40 o 110 o 75 o 40 o

6 Side 31 / Are the two ages cogruet? Side 32 / 180 Copeetary Ages are two ages with a su of 90 degrees. These two ages are copeetary ages because their su is 90. tice that they for a right age whe paced together. 105 o 75 o Side 33 / 180 Side 34 / 180 Copeetary Ages are two ages with a su of 90 degrees. 17 What is the easure of A? These two ages are copeetary ages because their su is 90. Athough they are't paced together, they ca sti be copeetary What is the easure of A? Side 35 / 180 Side 36 / Te whether the two ages are copeetary? Age 1 = 63 degrees Age 2 = 27 degrees

7 Side 37 / Te whether the ages are copeetary. Side 38 / 180 Suppeetary Ages are two ages with a su of 180 degrees. Age 1 = 146 degrees Age 2 = 44 degrees These two ages are suppeetary ages because their su is 180. tice that they for a straight age whe paced together. Side 39 / 180 Side 40 / 180 Suppeetary Ages are two ages with a su of 180 degrees. 21 What is the easureet of age A? These two ages are suppeetary ages because their su is 180. Athough they are't paced together, they ca sti be suppeetary. Age A 125 o Side 41 / 180 Side 42 / What is the easureet of age A? 23 Te whether the two ages are suppeetary. Age A 40 o Age 1 = 115 degrees Age 2 = 65 degrees

8 24 Fid the suppeet of Side 43 / Fid the copeet of Side 44 / Fid the copeet of Side 45 / Fid the suppeet of Side 46 / Fid the suppeet of Side 47 / Fid the copeet of Side 48 / 180

Side 49 / 180 Vertica Ages are two ages that are opposite each other whe two ies itersect.

a b d c b c a I this exape, the vertica ages are: Vertica ages have the sae easureet.

9 Side 49 / 180 Vertica Ages are two ages that are opposite each other whe two ies itersect. Side 50 / 180 Usig what you kow about vertica ages, fid the easure of the issig ages. a b d c b c a I this exape, the vertica ages are: Vertica ages have the sae easureet. So: By Vertica Ages: By Suppeetary Ages: Side 51 / 180 Side 52 / Are ages 2 ad 4 vertica ages? 31 Are ages 2 ad 3 vertica ages? Side 53 / 180 Side 54 / If age 1 is 60 degrees, what is the easure of age 3? You ust be abe to expai why. 33 If age 1 is 60 degrees, what is the easure of age 2? You ust be abe to expai why

Side 55 / 180 Adjacet Ages are two ages that are ext to each other ad have a coo ray betwee the. This eas that they are o the sae pae ad they share o itera poits. Adjacet or t Adjacet? You Decide!

10 Side 55 / 180 Adjacet Ages are two ages that are ext to each other ad have a coo ray betwee the. This eas that they are o the sae pae ad they share o itera poits. Adjacet or t Adjacet? You Decide! Side 56 / 180 A C is adjacet to How do you kow? They have a coo side (ray ) They have a coo vertex (poit B) b a a cick Adjacet to revea t cick Adjacet to revea t Adjacet b b a B D Side 57 / 180 Side 58 / Which two ages are adjacet to each other? 35 Which two ages are adjacet to each other? A 1 ad 4 A 3 ad 6 B 2 ad 4 B 5 ad P A Side 59 / 180 A trasversa is a ie that cuts across two or ore (usuay parae) ies. E Q Side 60 / 180 Correspodig Ages are o the sae side of the trasversa ad o the sae side of the give ies. I this diagra the correspodig ages are: c a Trasversa b d R F B A g e h f Iteractive Activity-Cick Here

Side 61 / 180 36 Which are pairs of correspodig ages? Side 62 / 180 37 Which are pairs of correspodig ages?

are pairs of correspodig ages? 39 Which pair of ages are ot correspodig?

o opposite sides of the trasversa ad o the outside of the give ies.

11 Side 61 / Which are pairs of correspodig ages? Side 62 / Which are pairs of correspodig ages? A 2 ad 6 A 2 ad 6 B 3 ad 7 C 1 ad B 3 ad 1 C 1 ad Side 63 / 180 Side 64 / Which are pairs of correspodig ages? 39 Which pair of ages are ot correspodig? A 1 ad 5 B 2 ad 8 C 4 ad A B C D E Side 65 / 180 Side 66 / 180 Aterate Exterior Ages are o opposite sides of the trasversa ad o the outside of the give ies. Aterate Iterior Ages are o opposite sides of the trasversa ad o the iside of the give ies. I this diagra the aterate exterior ages are: c a d b I this diagra the aterate iterior ages are: c a b d e f e f g h Which ie is the trasversa? g h

12 Side 67 / 180 Side 68 / 180 Sae Side Iterior Ages are o sae sides of the trasversa ad o the iside of the give ies. 40Are ages 2 ad 7 aterate exterior ages? I this diagra the sae side iterior ages are: c a b d g e h f Side 69 / Are ages 3 ad 6 aterate exterior ages? Side 70 / Are ages 7 ad 4 aterate exterior ages? Side 71 / 180 Side 72 / Which age correspods to age 5? 44Which pair of ages are sae side iterior? A B C D A B C D

13 Side 73 / What type of ages are ad? Side 74 / What type of ages are ad? A B Aterate Iterior Ages Aterate Exterior Ages A B Aterate Iterior Ages Aterate Exterior Ages C D E Correspodig Ages Vertica Ages Sae Side Iterior C D E Correspodig Ages Vertica Ages Sae Side Iterior Side 75 / 180 Side 76 / What type of ages are ad? A Aterate Iterior Ages B Aterate Exterior Ages C Correspodig Ages D Vertica Ages E Sae Side Iterior Are ages 5 ad 2 aterate iterior ages? Side 77 / 180 Side 78 / Are ages 5 ad 7 aterate iterior ages? 50Are ages 7 ad 2 aterate iterior ages? Pu

Side 79 / 180 51Are ages 3 ad 6 aterate exterior ages? Side 80 / 180 Specia Case!

14 Side 79 / Are ages 3 ad 6 aterate exterior ages? Side 80 / 180 Specia Case!!! If parae ies are cut by a trasversa the: Correspodig Ages are cogruet Aterate Iterior Ages are cogruet Aterate Exterior Ages are cogruet SO: Side 81 / 180 Side 82 / Give the easure of oe age, fid the easures of as ay ages as possibe. Which ages are cogruet to the give age? Type oe of the ito your respoder. 53Give the easure of oe age, fid the easures of as ay ages as possibe. What are the easures of the reaiig ages? Side 83 / 180 Side 84 / Give the easure of oe age, fid the easures of as ay ages as possibe. Which ages are cogruet to the give age? Type oe of the ito your respoder. 55Give the easure of oe age, fid the easures of as ay ages as possibe. What are the easures of the reaiig ages?

15 Side 85 / 180 Perieter & Circuferece Retur to Tabe of Cotets Side 86 / 180 Perieter Defiitio: The distace aroud a two-diesioa figure. w te: () represets the Legth, or oger side of the rectage. (w) represets the Width, or shorter side of the rectage. If o uits are give, use " u". w Side 87 / 180 Side 88 / 180 Perieter (P) of a rectage is foud by sovig the foowig forua: P = 2 + 2w Perieter (P) of a square is foud by doig four (4) ties Side (s): S P = 4s 56What is the Perieter (P) of the foowig rectage? 15 ft. 6 ft. Perieter of a poygo is the su of the egths of the sides. Side 89 / 180 Side 90 / What is the Perieter (P) of the square beow? 58What is the Perieter (P) of the figure? 7 8 i

16 Side 91 / What is the Perieter (P) of the figure? 8 c Side 92 / 180 Circuferece Defiitio: The outer boudary of a circe; the "perieter" of the circe. 10 c 12 c 3 c Circuferece Diaeter Side 93 / 180 The circuferece (C) of a circe is foud by usig oe of the foowig foruas: C = C = or C = 2 d or 2r r C = C = 2 Side 94 / 180 d or Diaeter (d): Ay straight ie seget that passes through the ceter poit of the circe, whose edpoits are o the circe. Radius (r): Ay ie seget fro the ceter poit of the circe, to ay poit o the circe---radius is 1/2 of the Diaeter. r Radius (R): Ay ie seget fro the ceter poit of the circe, to ay poit o the circe---radius is 1/2 of the Diaeter. C = C = 2 Side 95 / 180 d or Pi ( ), a atheatica costat, is the ratio of a circe's circuferece to its diaeter. r Side 96 / What is the Circuferece (C) of a circe with a radius (r) of 7c? (Use 3.14 for π) 7 c te:

17 Side 97 / What is the Circuferece (C) of a circe with a Diaeter (D) of 11i.? (Use 3.14 for π) Side 98 / Fid the circuferece of a circe whose radius is 2.5 eters. (Use 3.14 for π) 11 i. Side 99 / A circe has diaeter 8 yds. What is its circuferece? (Use 3.14 for π) Side 100 / The circuferece of a circe is c. What is its radius? (Use 3.14 for π) Side 101 / 180 Side 102 / 180 Area - The uber of square uits (uits 2 ) it takes to cover the surface of a figure. ALWAYS abe uits 2!!! Area of Rectages 12 ft Retur to Tabe of Cotets 6 ft

18 Side 103 / 180 How ay 1 ft 2 ties does it take to cover the rectage? Use the squares to fid out! Look for a faster way tha coverig the whoe figure. 12 ft Side 104 / 180 The Area (A) of a rectage is foud by usig the forua: A = egth(width) A = w The Area (A) of a square is foud by usig the forua: A = side(side) A = s 2 6 ft Side 105 / 180 Side 106 / What is the Area (A) of the figure? 66Fid the area of the figure beow. 15 ft 7 6 ft Side 107 / 180 Side 108 / 180 Area of a Paraeogra Let's use the sae process as we did for the rectage. How ay 1 ft 2 ties fit across the botto of the paraeogra? Area of Paraeogras Retur to Tabe of Cotets

Area of a Paraeogra. Side 109 / 180 Side 110 / 180 How does this hep us fid the area of the paraeogra?

4 ft 14 ft 14 ft How do you fid the area of a paraeogra? How ta is the paraeogra? How ca you te?

The Area (A) of a paraeogra is foud by usig the forua: Fid the area of the figure.

19 Area of a Paraeogra. Side 109 / 180 Side 110 / 180 How does this hep us fid the area of the paraeogra? Let's use the sae process as we did for the rectage. If we buid the paraeogra with rows of 14 ft 2, what happes? 4 ft 14 ft 14 ft How do you fid the area of a paraeogra? How ta is the paraeogra? How ca you te? Side 111 / 180 Side 112 / 180 Exape. The Area (A) of a paraeogra is foud by usig the forua: Fid the area of the figure. A = base(height) A = bh 4 c te: The base & height aways for a right age! 2.2 c 2.2 c 1.9 c 4 c cick to revea Side 113 / 180 Side 114 / 180 Try These. Fid the area of the figures Fid the area. 11 ft 10 ft ft cick to revea cick to revea 4

20 Side 115 / 180 Side 116 / Fid the area. 69 Fid the area. 17 i 7 12 i 10 i 12 i i 7 Side 117 / 180 Side 118 / Fid the area. 12 c 11 c 9 c Area of Triages Retur to Tabe of Cotets Side 119 / 180 Area of a Triage Let's use the sae process as we did for the rectage & paraeogra. How ay 1 ft 2 ties fit across the botto of the triage? Side 120 / 180 Area of a Triage If we cotiue to buid the triage with rows of 10 ft 2, what happes? 10 ft How ta is the triage? How ca you te?

Side 121 / 180 How does this hep us fid the area of the triage?

Side 122 / 180 4 ft 10 ft See that the rectage we buit is twice as arge as the triage.

Fid the area of the rectage, the divide by 2 20 ft 2 Side 123 / 180 The Area (A) of a

Side 124 / 180 te: The base & height aways for a right age!

21 Side 121 / 180 How does this hep us fid the area of the triage? Is this true for a triages? Let's see! Side 122 / ft 10 ft See that the rectage we buit is twice as arge as the triage. How do you fid the area of a triage? Cacuatig base(height) resuts i 2 triages! Fid the area of the rectage, the divide by 2 20 ft 2 Side 123 / 180 The Area (A) of a triage is foud by usig the forua: Exape. Fid the area of the figure. Side 124 / 180 te: The base & height aways for a right age! 4 c 10 c 10 c 6 c 12 4 cick to revea 24 Side 125 / 180 Side 126 / 180 Try These. 71 Fid the area. Fid the area of the figures. 13 ft 9 ft 12 ft 11 ft i 5 i 8 i 10 i cick to revea cick to revea

Side 127 / 180 Side 128 / 180 72 Fid the area 9 8 12 Area of Trapezoids 15 Retur to Tabe of Cotets Side

botto haf A paraeogra is created Side 130 / 180 The Area (A) of a trapezoid is foud by usig the forua:

Base 2 Base 2 Base 1 Side 131 / 180 Side 132 / 180 Exape. Fid the area of the figure. Try These.

22 Side 127 / 180 Side 128 / Fid the area Area of Trapezoids 15 Retur to Tabe of Cotets Side 129 / 180 Area of a Trapezoid Cut the trapezoid i haf horizotay Rotate the top haf so it ies ext to the botto haf A paraeogra is created Side 130 / 180 The Area (A) of a trapezoid is foud by usig the forua: See the diagras beow Base 1 Height te: The base & height aways for a right age! Base 2 Base 2 Base 1 Side 131 / 180 Side 132 / 180 Exape. Fid the area of the figure. Try These. Fid the area of the figures. 12 c 13 ft c 11 c 11 ft 9 ft 11 ft cick to revea 11 ft 20 9 c cick to revea cick to revea

Side 133 / 180 Side 134 / 180 73 Fid the area of the trapezoid. 74 Fid the area of the trapezoid. 4 22 c 6.

23 Side 133 / 180 Side 134 / Fid the area of the trapezoid. 74 Fid the area of the trapezoid c c c Side 135 / 180 Side 136 / 180 Area of a Circe The Area (A) of a Circe is foud by sovig the foowig forua: Area of Circes Retur to Tabe of Cotets Side 137 / 180 Side 138 / c Fid the area of the circe. A = π r 2 1. Substitute the radius ito forua. A = π (7) 2 2. Use 3.14 as a approxiatio for π. A = 3.14(49) A = c 2 75 What is the Area (A) of a Circe with a radius (r) of 8? 8 3. Do't forget to abe the uits as square uits.

24 Side 139 / What is the Area (A) of the circe? Side 140 / What is the Area (A) of the circe? Side 141 / A circuar spriker sprays water with a radius of 11 ft. How uch area ca the spriker cover? Side 142 / What is the area of a circe with a diaeter of 24 yds? Side 143 / What is the radius of a circe whose area is ? Side 144 / A circuar poo has a area of ft 2. What is its diaeter?

25 Side 145 / 180 Mixed Review: Perieter, Circuferece & Area Side 146 / Dr. Da wats to keep his kitte fro ruig through his fower bed by puttig up soe fecig. The fower bed is 10 ft. by 6ft. Wi Dr. Da eed to kow the area or the perieter of his fower bed to keep his kitty fro trapig the fowers? A B Area Perieter Retur to Tabe of Cotets Side 147 / 180 Side 148 / w sove the probe... 84Fid the perieter of the figure. Dr. Da wats to keep his kitte fro ruig through his fower bed by puttig up soe fecig. The fower bed is 10 ft. by 6ft. How uch fecig wi he eed? 5 c 4 c 3 c 4 c 11 c Side 149 / 180 Side 150 / Fid the area of the figure. 86Fid the perieter of the figure. 8 yd 4 yd 9 yd 8 yd 4 7

26 Side 151 / 180 Side 152 / Fid the circuferece of the figure. 88Fid the area of the figure. 9 i 5 i 12 i 12 i Side 153 / 180 Side 154 / Fid the area of the figure. 90Fid the perieter of the figure. 5 c 4 c 3 c 4 c 9 i 5 i 12 i 11 c Side 155 / 180 Side 156 / Fid the perieter of the figure. 92Fid the area of the figure. 8 yd 4 yd 8 yd 12 i 9 yd

27 93Fid the area of the figure. 4 7 Side 157 / 180 Side 158 / If you wat to pace a towe bar 9 3/4 iches og i the ceter of a door that is 27 1/2 iches wide, how far fro the edge of the door shoud you put the edge of the bar? Side 159 / A wa is 48" wide. You wat to ceter a picture frae that is 20" wide o the wa. How uch space wi there be betwee the edge of the wa ad the frae? Side 160 / 180 Side 161 / 180 Area of Irreguar Figures Retur to Tabe of Cotets Side 162 / 180 Area of Irreguar Figures Method #1 1. Divide the figure ito saer figures (that you kow how to fid the area of) 2. Labe each sa figure ad fid the area of each 3. Add the areas 4. Labe your aswer

28 Side 163 / 180 Side 164 / 180 Exape: Fid the area of the figure Area of Irreguar Figures Method #2 1. Create oe arge, cosed figure. 2. Labe the sa added figure ad fid the area Fid the area of the ew, arge figure 2 #1 # Subtract the areas 5. Labe your aswer Side 165 / 180 Side 166 / 180 Exape: Fid the area of the figure. 3 2 Try These: Fid the area of each figure Whoe Rectage 10 6 Extra Rectage ft 20 ft 8 ft 16 ft 10 Side 167 / 180 Side 168 / Fid the area. Top Rectage 97Fid the area. 2.5' 2.5' 5.25' 4' 1.5' 8.75' Botto Rectage Vertica Rectage Tota Area Whoe New Figure New Rectage Tota Area 7.75'

29 Side 169 / 180 Side 170 / Fid the area. 99Fid the area. Side Rectage 8 c 58 c Triage 4 ft. Botto Right Rectage 15 c 5 ft. Rectage 9 ft. Haf Circe Tota Area 6 ft. Tota Area Side 171 / 180 Side 172 / 180 Area of a Shaded Regio 1. Fid area of whoe figure. Area of Shaded Regios 2. Fid area of ushaded figure(s). 3. Subtract ushaded area fro whoe figure. 4. Labe aswer with uits 2 Retur to Tabe of Cotets Side 173 / 180 Side 174 / 180 Exape Try This Fid the area of the shaded regio. 20 ft Area Whoe Rectage Fid the area of the shaded regio. Area Whoe Square 7 ft 7 ft 15 ft Area Ushaded Square Area Circe Area Shaded Regio 14 c Area Shaded Regio

30 Side 175 / 180 Side 176 / 180 Try This Fid the area of the shaded regio. Area Trapezoid 100Fid the area of the shaded regio. Area Whoe Rectage Area Rectage 6' 2' 4' Area Ushaded 8 2 Area Shaded Regio Area Shaded Regio 8' Side 177 / 180 Side 178 / Fid the area of the shaded regio. 102Fid the area of the shaded regio. Area Paraeogra 8" Area Whoe 11" Area Triage 14" 8" Area Rectage 8" 7" 6" 4" 6" 12" Area Shaded Regio 12" Area Shaded Regio Side 179 / 180 Side 180 / Fid the area of the shaded regio. Area Circe 104A ceet path 3 feet wide is poured aroud a rectaguar poo. If the poo is 15 feet by 7 feet, how uch ceet was eeded to create the path? Area Path & Poo 4 yd Area Triage Area Poo Area Shaded Regio Area Path

UNIT 4C Itera,on: Correctness and Efficiency. General Idea: Any one Itera,on. i L SORTED SORTED

UNIT 4C Itera,on: Correctness and Efficiency. General Idea: Any one Itera,on. i L SORTED SORTED UNIT 4C Itera,o: Correctess ad Efficiecy 1 L Geeral Idea: Ay oe Itera,o SORTED i i L SORTED 2 1 Look Closer at Iser,o Sort Give a list L of legth, > 0. 1. Set i = 1. 2. While i is ot equal to, do the followig: