AREA OF SOLIDS Metric Units UP the stairs

AREA OF SOLIDS

Metric Units UP the stairs you move decimal to the LEFT km hm dam m DOWN the stairs you move decimal to the RIGHT dm cm mm DRUL = Down Right, Up Left For each step you move the decimal 1 place left or right depending on how you are moving

UNITS OF AREA km 2 hm 2 dam 2 dm 2 cm 2 mm 2 Each step requires moving 2 decimal places because …. AREA is 2 dimensional Follow the DRUL rules…down right up left.

Practise converting units 1345 mm = 0. 895 hm = 45. 256 km = 43. 664 m = 7895. 209 dm = _____m ____ mm ____ dam ____ cm ____ hm 678. 34 km 2= 34. 56 m 2 = 445. 998 km 2 = 57980. 3 mm 2 = 0. 94857 dam 2= ____ dam 2 ____ cm 2 ____ hm 2 ____dm 2 Workbook page 177 #1, 2 91 - for Thursday 4306 – for Wednesday 306 -05 for wednesday

Answers 1. 345 89500 4525. 6 4366. 4 7. 895209 6783400 345600 44599. 8 0. 0579803 9485. 7

Area of a Prism 4 cm 2 cm 8 cm Step 3 – Find TA (total area) TA = Area of the bases + LA TA = 2(16) cm 2+ 80 cm 2 TA = 32 + 80 TA = 112 cm 2 Step 1 – Find Area of Base Abase = 8 cm x 2 cm Abase = 16 cm 2 Step 2 – Find the LA LA = Perimeter of base x height LA = 20 cm x 4 cm LA = 80 cm 2

Can you find the area of the base when it’s a regular polygon? c c = cote (side length) a = apothem n= number of sides a n Yes…you CAN too !!!!! Area = C A N 2

Example Find the area of the base of a regular hexagonal prism. c = 10 cm a=8. 7 cm n = 6 sides Area base = can 2 A base = 10 x 8. 7 x 6 2 A base = 522 2 A base = 261 cm 2

Find the total area of this prism Pentagonal prism that has a height of 3 cm c = 20 cm a = 4 cm n = 5 sides Step 1 – Find Area 1 Base Abase = c a n 2 Abase = 20 x 4 x 5 2 Abase = 400 2 Abase = 200 cm 2 Step 2 – Find the LA LA = Pb x h LA = (20 x 5) x 3 LA = 100 x 3 LA = 300 cm 2 Step 3 – Find the Total Area of the prism TA prism = LA + 2(Abase) TA prism = 300 cm 2 + 2 (200 cm 2) TA prism = 300 cm 2 + 400 cm 2 TA prism = 700 cm 2 Workbook page 178 # 3, 4, 5

Page 178 #3, 4, 5 #3 4. 5 cm Step 1 – Find Area of Base Abase = L x W Abase = 4. 5 x 4. 5 Abase = 20. 25 cm 2 Step 2 – Find the LA LA = Perimeter of base x height LA = (4. 5 x 4) x 4. 5 cm LA = 18 cm x 4. 5 cm LA = 81 cm 2 Step 3 – Find the Total Area TA = 2(Abase ) + LA TA = 2(20. 25) + 81 TA= 121. 5 cm 2

Answers to Workbook Page 178 #4 a) 72. 72 cm 2 b) 108 cm 2 c) 190. 8 cm 2 #5) 286. 08 cm 2 Page 179 #6) 844. 71 cm 2 # 7) 1107 cm 2 #8) 384 cm 2 Answers to Text book #2 Page 66 #2 a) 15. 12 cm 2 Page 67 #3 a) 238. 77 cm 2 2140 cm 2 #5 a) 1649. 36 cm 2 b) 389. 10 cm 2 c)

Page 179 #7 9 cm a= 6. 2 cm Area of base = can 2 Area of base = 9 x 6. 2 x 5 2 Area of base = 279 2 Area of base = 139. 5 cm 2 LA= Pb x height LA= (9 x 5) x 18. 4 LA = 45 x 18. 4 LA = 828 cm 2 TA = 2(Area of base) + LA TA = 2(139. 5) + 828 TA = 279 + 828 TA = 1107 cm 2

r =10 mm Area of a Cylinder Height = 50 mm Workbook Page 181 #14 a, b, c #15 Text #2 Page 66 #2 a Page 67 #3 a, b, c #5 a Page 68 #9 b Step 1 – Find Area of Bases Base is a circle…. Area = π r 2 Abase = π(102) Abase = 314. 16 mm 2 Step 2 – Find the Lateral Area LA = Circumference of base x Height LA = 2πr x Height LA = 2π(10) x 50 LA = 62. 83 x 50 LA = 3141. 59 mm 2 Step 3 – find the total area of the cylinder TA = LA + 2 Abase TA = 3141. 59 + 2(314. 16) TA = 3141. 59 + 628. 32 TA = 3769. 91 mm 2

Area of Pyramid Apothem 15 cm Square base 12 cm Workbook Page 182 #18 to 22 Textbook #2 Page 66 #1 c Page 67 #4 Step 1 –find area of base A=Lx. W A = 12 x 12 A = 144 cm 2 Step 2 – Find LA LA = Pb x apothem 2 LA = 48 x 15 2 LA = 360 cm 2 Step 3 – Total Area TA = LA + Area of Base TA = 360 + 144 TA = 504 cm 2

Area of a Cone height apothem = 12 radius= 4. 5 cm Workbook Page 184 # 27 -34 Step 1 – Find Area of Base Area of base = πr 2 Area of base = π (4. 52) Area of base = 63. 62 cm 2 Step 2 – Find the LA LA = π r x apothem LA = π (4. 5) ( 12) LA = 169. 5 cm 2 Step 3 – Find the TA TA = LA + Area of base TA = 169. 5 + 63. 62 TA = 233. 27 cm 2

How to find the dimensions of the sector of a circle a s r r=a s 360

Area of a Sphere r = 7 cm TA = LA = 4πr 2 r TA = 4 π (72) TA = 615. 75 cm 2 What is the radius of a sphere that has an area of 452. 39 cm 2