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Geometry Surface Area Calculations

Learn how to find the surface areas of prisms and cylinders using formulas and examples in this geometry lesson.

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Geometry Surface Area Calculations

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  1. Transparency 7 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

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

  4. 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)]

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

  6. Example 7-1a Find the surface area of the rectangular prism. A = L  W First find the area of the base A = 15 mm  9 mm Base is a rectangle so write formula for area of a rectangle mm2 A = 135 Replace L with 15 mm Replace W with 9 mm Multiply numbers Multiply units 1/3

  7. Example 7-1a Find the surface area of the rectangular prism. Area of base = 135 mm2 Area of top = 135 mm2 The top of prism has the same dimensions as the base so they will have the same area Second part of surface area is finding the perimeter and multiplying that by the height of the prism 1/3

  8. Example 7-1a Find the surface area of the rectangular prism. Area of base = 135 mm2 Area of top = 135 mm2 SA lateral = [(2L + 2W)  height of prism] Write formula for perimeter of rectangle times height of prism This is lateral surface area 1/3

  9. Example 7-1a Find the surface area of the rectangular prism. Area of base = 135 mm2 Area of top = 135 mm2 SA lateral = [(2L + 2W)  height of prism]  7 mm] SA lateral = [(2  15 mm + 2  9 mm) Replace L with 15 mm Replace W with 9 mm Replace height of prism with 7 mm 1/3

  10. Example 7-1a Find the surface area of the rectangular prism. Area of base = 135 mm2 Follow order of operations P E MD AS Area of top = 135 mm2 SA lateral = [(2L + 2W)  height of prism]  7 mm] SA lateral = [(2  15 mm + 2  9 mm) Work inside parenthesis + 18 mm)  7 mm] SA lateral = [(30 mm Inside parenthesis do multiplication first Bring down rest of equation 1/3

  11. Example 7-1a Find the surface area of the rectangular prism. Area of base = 135 mm2 Follow order of operations P E MD AS Area of top = 135 mm2 SA lateral = [(2L + 2W)  height of prism]  7 mm] SA lateral = [(2  15 mm + 2  9 mm) + 18 mm)  7 mm] SA lateral = [(30 mm  7 mm SA lateral = 48 mm Work inside parenthesis Bring down rest of equation 1/3

  12. Example 7-1a Find the surface area of the rectangular prism. Area of base = 135 mm2 Area of top = 135 mm2 SA lateral = [(2L + 2W)  height of prism]  7 mm] SA lateral = [(2  15 mm + 2  9 mm) + 18 mm)  7 mm] SA lateral = [(30 mm  7 mm SA lateral = 48 mm Multiply numbers mm2 Multiply units SA lateral = 336 1/3

  13. Example 7-1a Find the surface area of the rectangular prism. Area of base = 135 mm2 Area of top = 135 mm2 Add the areas together SA lateral = 336 mm2 Answer: Surface Area = 606 mm2 1/3

  14. Example 7-1b Find the surface area of the rectangular prism. Answer: Surface Area = 142 cm2 1/3

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

  16. Example 7-2a  5.8 ft  5 ft A = 14.5 ft2 Replace b with 5 ft Replace h with 5.8 ft Multiply numbers Multiply units 2/3

  17. Example 7-2a Area of triangle = 14.5 ft2 Area of triangle = 14.5 ft2 SAlateral = Perimeter  Height of prism The front of prism has the same dimensions as the back so they will have the same area Second part of surface area is finding the perimeter and multiplying that by the height of the prism 2/3

  18. Example 7-2a Area of triangle = 14.5 ft2 Area of triangle = 14.5 ft2 SAlateral = Perimeter  Height of prism SAlateral = (S1 + S2 + S3)  Height of prism SAlateral = (6.3 ft + 6.3 ft + 5 ft) Write formula for perimeter of rectangle times height of prism Replace S1 and S2 with 6.3 ft Replace S3 with 5 ft 2/3

  19. Example 7-2a Area of triangle = 14.5 ft2 Area of triangle = 14.5 ft2 SAlateral = Perimeter  Height of prism SAlateral = (S1 + S2 + S3)  Height of prism SAlateral = (6.3 ft + 6.3 ft  5.8 ft + 5 ft) Replace Height of Prism with 5.8 ft 2/3

  20. Example 7-2a Follow order of operations P E MD AS Area of triangle = 14.5 ft2 Work inside parenthesis Area of triangle = 14.5 ft2 SAlateral = Perimeter  Height of prism SAlateral = (S1 + S2 + S3)  Height of prism SAlateral = (6.3 ft + 6.3 ft + 5 ft)  5.8 ft SAlateral = 17.6 ft  5.8 ft Add SAlateral = 102.08 Multiply numbers ft2 Multiply units 2/3

  21. Example 7-2a Area of triangle = 14.5 ft2 Add the areas together Area of triangle = 14.5 ft2 SAlateral = 102.08 ft2 Answer: Surface Area = 131.08 ft2 2/3

  22. Example 7-2c DECORATINGJulia is painting triangular prisms to use as decoration in her garden. Find the surface area of the prism. Answer: Surface Area = 85.5 in2 2/3

  23. Example 7-3a Find the surface area of the cylinder. Round to the nearest hundredth. A = r2 A =   (2.5 m)2 First find the area of the base Remember: a cylinder as a circle for a base Write formula for area of circle Replace r with 2.5 m since radius is half the diameter 3/3

  24. Example 7-3a Find the surface area of the cylinder. Round to the nearest hundredth. A = r2 A =   (2.5 m)2 Follow order of operations P E MD AS A =   6.25 m2 A = 19.63 m2 Evaluate exponent (2.5 m)2 Multiply 3/3

  25. Example 7-3a Find the surface area of the cylinder. Round to the nearest hundredth. Area of Circle = 19.63 m2 Area of Circle = 19.63 m2 The front of the cylinder has the same dimensions as the back so they will have the same area Second part of surface area is finding the circumference and multiplying that by the height of the cylinder 3/3

  26. Example 7-3a Find the surface area of the cylinder. Round to the nearest hundredth. Area of Circle = 19.63 m2 Area of Circle = 19.63 m2 SAlateral = Circumference  Height of Cylinder SAlateral = (d)  Height of Cylinder SAlateral = (  5 m)  2 m Write formula for circumference of circle times height of cylinder Replace d with 5 m Replace Height of Cylinder with 2 m 3/3

  27. Example 7-3a Find the surface area of the cylinder. Round to the nearest hundredth. Area of Circle = 19.63 m2 Area of Circle = 19.63 m2 SAlateral = Circumference  Height of Cylinder SAlateral = (d)  Height of Cylinder SAlateral = (  5 m)  2 m Follow order of operations P E MD AS SAlateral = 15.71 m  2 m Work inside parenthesis Multiply 3/3

  28. Example 7-3a Find the surface area of the cylinder. Round to the nearest hundredth. Area of Circle = 19.63 m2 Area of Circle = 19.63 m2 SAlateral = Circumference  Height of Cylinder SAlateral = (d)  Height of Cylinder SAlateral = (  5 m)  2 m Multiply numbers Multiply units SAlateral = 15.71 m  2 m SAlateral = 31.42 m2 3/3

  29. Example 7-3a Find the surface area of the cylinder. Round to the nearest hundredth. Area of Circle = 19.63 m2 Area of Circle = 19.63 m2 SAlateral = 31.42 m2 Add the areas together Answer: Surface Area = 70.68 m2 3/3

  30. Example 7-3b * Find the surface area of the cylinder. Round to the nearest hundredth. Answer: Surface Area = 207.34 mm2 3/3

  31. End of Lesson 7 Assignment

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