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Example 7-3b Objective Find the surface areas of prisms and cylinders

Example 7-3b Vocabulary Surface Area The sum of the area of the base(s) and the perimeter times the height of the figure! Surface Area = [2(Area of Base)] + [(Perimeter of Base  Height of figure)]

Lesson 7 Contents Example 1Surface Area of a Rectangular Prism Example 2Surface Area of a Triangular Prism Example 3Surface Area of a Cylinder

Example 7-1a Find the surface area of the rectangular prism. First find the area of the base Replace L with 15 mm Base is a rectangle so write formula for area of a rectangle A = L  W 1/3 A = 15 mm Replace W with 9 mm  9 mm Multiply numbers A = 135 Multiply units mm 2

Example 7-1a Find the surface area of the rectangular prism. The top of prism has the same dimensions as the base so they will have the same area 1/3 Area of base = 135 mm 2 Area of top = 135 mm 2 Second part of surface area is finding the perimeter and multiplying that by the height of the prism

Example 7-1a Find the surface area of the rectangular prism. 1/3 Area of base = 135 mm 2 Area of top = 135 mm 2 SA lateral = [(2L + 2W)  height of prism] Write formula for perimeter of rectangle times height of prism This is lateral surface area

Example 7-1a Find the surface area of the rectangular prism. 1/3 Area of base = 135 mm 2 Area of top = 135 mm 2 SA lateral = [(2L + 2W)  height of prism] Replace L with 15 mm SA lateral = [(2  15 mm Replace W with 9 mm + 2  9 mm) Replace height of prism with 7 mm  7 mm]

+ 18 mm)  7 mm] Example 7-1a Find the surface area of the rectangular prism. 1/3 Area of base = 135 mm 2 Area of top = 135 mm 2 SA lateral = [(2L + 2W)  height of prism] Follow order of operations P E MD AS SA lateral = [(2  15 mm+ 2  9 mm)  7 mm] Work inside parenthesis Inside parenthesis do multiplication first SA lateral = [(30 mm Bring down rest of equation

+ 18 mm)  7 mm] Example 7-1a Find the surface area of the rectangular prism. 1/3 Area of base = 135 mm 2 Area of top = 135 mm 2 SA lateral = [(2L + 2W)  height of prism] Follow order of operations P E MD AS SA lateral = [(2  15 mm+ 2  9 mm)  7 mm] SA lateral = [(30 mm Work inside parenthesis SA lateral = 48 mm Bring down rest of equation  7 mm

+ 18 mm)  7 mm] Example 7-1a Find the surface area of the rectangular prism. 1/3 Area of base = 135 mm 2 Area of top = 135 mm 2 SA lateral = [(2L + 2W)  height of prism] SA lateral = [(2  15 mm+ 2  9 mm)  7 mm] SA lateral = [(30 mm Multiply numbers SA lateral = 48 mm Multiply units  7 mm SA lateral = 336 mm 2

Example 7-1a Find the surface area of the rectangular prism. 1/3 Area of base = 135 mm 2 Area of top = 135 mm 2 Add the areas together SA lateral = 336 mm 2 Surface Area = 606 mm 2 Answer:

Example 7-1b Find the surface area of the rectangular prism. Answer: Surface Area = 142 cm 2 1/3

Example 7-2a CAMPING A family wants to reinforce the fabric of its tent with a waterproofing treatment. Find the surface area, including the floor, of the tent below. 2/3 First find the area of the base Base is a triangle Write formula for area of triangle

Example 7-2a 2/3 Replace b with 5 ft  5 ft Replace h with 5.8 ft  5.8 ft Multiply numbers A = 14.5 Multiply units ft 2

Example 7-2a 2/3 Area of triangle = 14.5 ft 2 The front of prism has the same dimensions as the back so they will have the same area Area of triangle = 14.5 ft 2 Second part of surface area is finding the perimeter and multiplying that by the height of the prism SA lateral = Perimeter  Height of prism

Example 7-2a 2/3 Area of triangle = 14.5 ft 2 SA lateral = Perimeter  Height of prism Write formula for perimeter of rectangle times height of prism SA lateral = (S 1 + S 2 + S 3 )  Height of prism Replace S 1 and S 2 with 6.3 ft SA lateral = (6.3 ft ft Replace S 3 with 5 ft + 5 ft)

Example 7-2a 2/3 Area of triangle = 14.5 ft 2 SA lateral = Perimeter  Height of prism SA lateral = (S 1 + S 2 + S 3 )  Height of prism Replace Height of Prism with 5.8 ft SA lateral = (6.3 ft ft + 5 ft)  5.8 ft

Example 7-2a 2/3 Area of triangle = 14.5 ft 2 SA lateral = Perimeter  Height of prism SA lateral = (S 1 + S 2 + S 3 )  Height of prism SA lateral = (6.3 ft ft + 5 ft)  5.8 ft Follow order of operations P E MD AS Work inside parenthesis Add SA lateral = 17.6 ft  5.8 ft Multiply numbers SA lateral = Multiply units ft 2

Example 7-2a 2/3 Area of triangle = 14.5 ft 2 SA lateral = ft 2 Add the areas together Surface Area = ft 2 Answer:

Example 7-2c DECORATING Julia is painting triangular prisms to use as decoration in her garden. Find the surface area of the prism. Answer: Surface Area = 85.5 in 2 2/3

Example 7-3a Find the surface area of the cylinder. Round to the nearest hundredth. 3/3 First find the area of the base Remember: a cylinder as a circle for a base Write formula for area of circle A =  r 2 Replace r with 2.5 m since radius is half the diameter A =   (2.5 m) 2

Example 7-3a Find the surface area of the cylinder. Round to the nearest hundredth. 3/3 A =  r 2 A =   (2.5 m) 2 Follow order of operations P E MD AS Evaluate exponent (2.5 m) 2 A =   6.25 m 2 Multiply A = m 2

Example 7-3a Find the surface area of the cylinder. Round to the nearest hundredth. 3/3 Area of Circle = m 2 The front of the cylinder has the same dimensions as the back so they will have the same area Area of Circle = m 2 Second part of surface area is finding the circumference and multiplying that by the height of the cylinder

Example 7-3a Find the surface area of the cylinder. Round to the nearest hundredth. 3/3 Area of Circle = m 2 SA lateral = Circumference  Height of Cylinder Write formula for circumference of circle times height of cylinder SA lateral = (  d)  Height of Cylinder Replace d with 5 m SA lateral = (   5 m) Replace Height of Cylinder with 2 m  2 m

Example 7-3a Find the surface area of the cylinder. Round to the nearest hundredth. 3/3 Area of Circle = m 2 SA lateral = Circumference  Height of Cylinder SA lateral = (  d)  Height of Cylinder SA lateral = (   5 m)  2 m Follow order of operations P E MD AS Work inside parenthesis Multiply SA lateral = m  2 m

Example 7-3a Find the surface area of the cylinder. Round to the nearest hundredth. 3/3 Area of Circle = m 2 SA lateral = Circumference  Height of Cylinder SA lateral = (  d)  Height of Cylinder SA lateral = (   5 m)  2 m Multiply numbers SA lateral = m  2 m SA lateral = Multiply units m2m2

Example 7-3a Find the surface area of the cylinder. Round to the nearest hundredth. 3/3 Area of Circle = m 2 SA lateral = m 2 Add the areas together Surface Area = m 2 Answer:

Example 7-3b Find the surface area of the cylinder. Round to the nearest hundredth. Answer: * Surface Area = mm 2 3/3

End of Lesson 7 Assignment Lesson 7:7 Surface Area of Prisms and Cylinders All