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Understanding Total Surface Area of Rectangular, Triangular, and Hexagonal Prisms

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This guide explores the concept of Total Surface Area (TSA) for various prisms, including rectangular, triangular, and hexagonal shapes. It provides detailed calculations for each prism type, demonstrating how to find the TSA through formulas and breakdowns of the shapes involved. Focusing on examples with dimensions, the guide clarifies the number of sides and the formulas needed, utilizing practical visuals to explain how to approach real-world problems concerning surface area. Perfect for students and enthusiasts alike!

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Understanding Total Surface Area of Rectangular, Triangular, and Hexagonal Prisms

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Presentation Transcript

  1. Total Surface Area

  2. What is the Total Surface Area? Rectangular Prism 5 “ 4 “ 6 “

  3. How many sides? Rectangular Prism 5 “ 4 “ 6 “

  4. How many sides? 6 Rectangular Prism 5 “ Front & Back Top & Bottom Left & Right 4 “ 6 “

  5. How many sides? 6 Rectangular Prism 5 “ Front & Back Top & Bottom Left & Right = 6 · 5 = 30 = 6 · 4 = 24 = 4 · 5 = 20 4 “ 6 “

  6. How many sides? 6 Rectangular Prism 5 “ Front & Back Top & Bottom Left & Right = 6 · 5 = 30 = 6 · 4 = 24 = 4 · 5 = 20 = 2 · 74 = 148 in2 Two of each side 4 “ TSA 6 “

  7. Rectangular Prism 8 cm What is the TSA? 40 cm 10 cm

  8. Rectangular Prism 8 cm 10 · 8 = 80 10 · 40 = 400 40 · 8 = 320 = 2 · 800 TSA = 1600 cm2 40 cm 10 cm

  9. Triangular Prism What is the TSA? 10’ 5’ 6’

  10. Triangular Prism How many sides? 10’ 5’ 6’

  11. Triangular Prism How many sides? 5 Two triangles Three rectangles 10’ 5’ 6’

  12. Triangular Prism 2D : 2 · ½ 6 · 5 = 30 S1 : 6 · 10 = 60 S2 : 5 · 10 = 50 S3 : ? · 10 = ? How do you find this side? 10’ 5’ 6’

  13. Triangular Prism 2D : 2 · ½ 6 · 5 = 30 S1 : 6 · 10 = 60 S2 : 5 · 10 = 50 S3 : ? · 10 = ! Pythagorean Thm 10’ 5’ 6’

  14. Triangular Prism 2D : 2 · ½ 6 · 5 = 30 S1 : 6 · 10 = 60 S2 : 5 · 10 = 50 S3 : ? · 10 = 52 + 62 = c2 25 + 36 = c2 61 = c2 7.810 = c 10’ 5’ 6’

  15. Triangular Prism 2D : 2 · ½ 6 · 5 = 30 S1 : 6 · 10 = 60 S2 : 5 · 10 = 50 S3 : 7.810 · 10 = 78.10 TSA = 218.10 ft2 10’ 5’ 6’

  16. Triangular Prism TSA? 10m 25m 6m

  17. Triangular Prism 2D : 2 · ½ 6 · ? = ____ S1 : 10 · 25 = 250 S2 : 10 · 25 = 250 S3 : 6 · 25 = 150 10m ? How do you find the height 25m 6m

  18. Triangular Prism 2D : 2 · ½ 6 · ? = ____ S1 : 10 · 25 = 250 S2 : 10 · 25 = 250 S3 : 6 · 25 = 150 10m ! Pythagorean Thm 25m 6m

  19. Triangular Prism 2D : 2 · ½ 6 · ? = ____ S1 : 10 · 25 = 250 S2 : 10 · 25 = 250 S3 : 6 · 25 = 150 10m 102 – 32 = a2 100 – 9 = a2 91 = a2 9.539 = a 25m 6m

  20. Triangular Prism 2D : 2 · ½ 6 · 9.539 = 57.236 S1 : 10 · 25 = 250 S2 : 10 · 25 = 250 S3 : 6 · 25 = 150 TSA = 707.24 m2 10m 25m 6m

  21. Hexagonal Prism TSA? 15m 5m

  22. Hexagonal Prism How many sides? 15m 5m

  23. Hexagonal Prism How many sides? 8 2 hexagons 6 rectangles 15m 5m

  24. Hexagonal Prism 2 hexagons - 2 ½ ans 6 rectangles – 6 l · w ? How do you get the apothem 15m 5m

  25. Hexagonal Prism 2 hexagons - 2 ½ ans 6 rectangles – 6 l · w ! 30-60-90 triangle or Pythagorean thm 15m 5m

  26. Hexagonal Prism 2 hexagons - 2 ½ ans 6 rectangles – 6 l · w The apothem is 2.5Ö(3) ! 30-60-90 triangle or Pythagorean thm 15m 2.5 5m

  27. Hexagonal Prism 2 hex - 2 · ½ ·2.5Ö(3)· 6 · 5 6 rect – 6 · 5 · 15 The apothem is 2.5Ö(3) ! 30-60-90 triangle or Pythagorean thm 15m 2.5 5m

  28. Hexagonal Prism 2 · ½ ·2.5Ö(3)· 6 · 5 = 129.904 6 · 5 · 15 = 450 TSA = 579.90m2 The apothem is 2.5Ö(3) ! 30-60-90 triangle or Pythagorean thm 15m 2.5 5m

  29. What is the TSA? Cylinder 5m 15m

  30. What does this look like “Cut” apart? Cylinder 5m 15m

  31. Two circles and a rectangle Cylinder 15m What is the length of the rectangle? 5m

  32. Cylinder 15m The length of the rectangle is the CIRCUMFERENCE of the circle. 5m

  33. Cylinder 15m 2pr 5m

  34. Cylinder 15m 2 circles: 2 p· 52 = 157.080 Rectangle: 2 p 5 · 15 =471.239 TSA = 628.32 5m

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