AREA OF SOLIDS

Area of a Prism Step 1 – Find Area of Base Abase = 8cm x 2 cm Step 2 – Find the LA LA = Perimeter of base x height LA = 20 cm x 4 cm LA = 80 cm2 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

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

Example Find the area of the base of a regular hexagonal prism. Area base = can 2 A base = 10 x 8.7 x 6 A base = 522 A base = 261 cm2 c = 10 cm a=8.7 cm n = 6 sides

Find the total surface area of this prism Pentagonal prism that has a height of 3cm Step 1 – Find Area 1 Base Abase = c a n 2 Abase = 20 x 4 x 5 Abase = 400 Abase = 200cm2 Step 2 – Find the LA LA = Pb x h LA = (20 x 5) x 3 LA = 100 x 3 LA = 300 cm2 c = 20 cm n = 5 a = 4 cm

TA prism = LA + 2(Abase) TA prism = 300 cm2 + 2 (200 cm2) Step 3 – Find the Total Area of the prism TA prism = LA + 2(Abase) TA prism = 300 cm2 + 2 (200 cm2) TA prism = 300 cm2 + 400 cm2 TA prism = 700 cm2 Workbook page 178 # 3,4,5

Answers to Workbook Page 178 #4a) 72.72cm2 b) 108cm2 c) 190.8cm2 #5) 286.08cm2 Page 179 #6) 844.71cm2 # 7) 1107cm2 #8) 384cm2

Page 179 #7 Area of base = can 2 9cm Area of base = 9 x 6.2 x 5 Area of base = 139.5 cm2 9cm a= 6.2cm LA= Pb x height LA= (9 x 5) x 18.4 LA = 45 x 18.4 LA = 828 cm2 TA = 2(Area of base) + LA TA = 2(139.5) + 828 TA = 279 + 828 TA = 1107 cm2

Area of a Cylinder Step 1 – Find Area of Bases Base is a circle…. Height = 50 mm r =10 mm Step 1 – Find Area of Bases Base is a circle…. Area = π r2 Abase = π(102) Abase = 314.16mm2 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 mm2

Step 3 – find the total area of the cylinder TA = LA + 2 Abase TA = 3769.91 mm2 Workbook Page 181 #14a,b,c #15

Area of Pyramid Step 1 –find area of base A = L x W A = 12 x 12 Square base 12cm Apothem 15cm Step 1 –find area of base A = L x W A = 12 x 12 A = 144 cm2 Step 2 – Find LA LA = Pb x apothem 2 LA = 48 x 15 LA = 360 cm2

Step 3 – Total Area TA = LA + Area of Base TA = 360 + 144 TA = 504 cm2 Workbook Page 182 #18 to 22

Area of a Cone Step 1 – Find Area of Base Area of base = πr2 height apothem = 12 radius= 4.5 cm Step 1 – Find Area of Base Area of base = πr2 Area of base = π (4.52) Area of base = 63.62 cm2 Step 2 – Find the LA LA = π r x apothem LA = π (4.5) ( 12) LA = 169.5 cm2 Workbook Page 184 # 27-34

Step 3 – Find the Total Surface Area TA = LA + Area of base TA = 169.5 + 63.62 TA = 233.27 cm2

Area of a Sphere r = 7cm TA = LA = 4πr2 TA = 4 π (72) TA = 615.75cm2 r