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Surface Area

Surface Area. 6.3.1.1 Calculate the surface area and volume of prisms and use appropriate units, such as cm 2 and cm 3 . Justify the formulas used. Justification my involve decomposition, nets, or other models. 10.6 Notes. Surface Area of a Prism.

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Surface Area

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  1. Surface Area 6.3.1.1 Calculate the surface area and volume of prisms and use appropriate units, such as cm2 and cm3. Justify the formulas used. Justification my involve decomposition, nets, or other models.

  2. 10.6 Notes Surface Area of a Prism • Surface area is found by finding the area of all the sidesand then adding those answers up. • Ask yourself how many faces there are • Divide the prism into individual shapes if you need to • Draw a net of the shape if you need to Helpful Hints

  3. I can… • Determine the surface area of rectangular prisms • Determine the surface area of triangular prisms Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

  4. Surface Area • What does it mean to you? • Does it have anything to do with what is in the inside of the prism.? • Surface area is found by finding the area of all the sidesand then adding those answers up. • How will the answer be labeled? • Units2 because it is area!

  5. 4 cm 7 cm 10 cm Do you see the RED face? What are the dimensions of this rectangle? 4 cm 10 cm

  6. 4 cm 7 cm 10 cm Do you see another face that is just like the RED face? Where is it located?

  7. 4 cm 4 cm 10cm 10cm Yes, it’s on the back.

  8. 40cm2 40cm2 Now there are 2 rectangles that each have an area of 40 sq. cm

  9. 4 cm 7 cm 10 cm Do you see the BLUE face? What are the dimensions of this rectangle? 4 cm 7 cm

  10. 4 cm 7 cm 10 cm Do you see another face that is just like the BLUE face? Where is it located?

  11. 4 cm 4 cm 7 cm 7 cm Yes, it’s on the left side.

  12. 28cm2 28cm2 Now there are 2 rectangles that each have an area of 28 sq. cm.

  13. 4cm 7 cm 10cm Do you see the GREEN face? What are the dimensions of this rectangle? 7 cm 10 cm

  14. 4 cm 7 cm 10 cm Do you see another face that is just like the GREEN face? Where is it located?

  15. 7 cm 7 cm 10cm 10cm Yes, it’s on the bottom.

  16. 70cm2 70cm2 Now there are 2 rectangles that each have an area of 70 sq. cm.

  17. 40cm2 40cm2 28cm2 + + 28cm2 + 70cm2 + 70cm2 Now we just need to add all the areas of the sides together.

  18. The total Surface Area for this rectangular prism is 40 + 40 + 28 + 28 + 70+70 = 276cm2

  19. top side front 5 in 6 in 4 in Rectangular Prism How many faces are on here? 6 Find the area of each of the faces. Do any of the faces have the same area? front = 5 x 4 = 20 If so, which ones? back = 5 x 4 = 20 Opposite faces are the same. left side = 6 x 5 = 30 right side = 6 x 5 = 30 148 in2 Find the SA top = 4 x 6 = 24 bottom = 4 x 6 = 24

  20. Cube Are all the faces the same? YES A How many faces are there? 4m 6 Find the Surface area of one of the faces. 4 x 4 = 16 Take that times the number of faces. X 6 96 m2

  21. Triangular Prism 5 How many faces are there? 4 5 How many of each shape does it take to make this prism? 10 m 3 2 triangles and 3 rectangles 4 x 3 2 b x h 2 Find the surface area. Start by finding the area of the triangle. = 6 x 2= 12 How many triangles were there? 5 x 10 = 50 = side 1 4 x 10 = 40 = side 2 3 x 10 = 30 = side 3 2 Find the area of the 3 rectangles. 30+40+50 = 120 Total SA = 120 + 12 = 132 m2

  22. Simple Method Find the surface area of the triangular prism. 5 ft 8 ft 20 ft 10 ft

  23. You can always cut the prism into individual shapes 8 ft 5 ft 10 ft 20 ft 20 ft 5 ft 8 ft 10 ft 20 ft 10 ft

  24. You can always cut the prism into individual shapes 8 ft 5 ft 10 ft 20 ft 20 ft 40 sq ft 100 sq ft 5 ft 8 ft 10 ft 20 ft 10 ft 200 sq ft 40 sq ft 100 sq ft

  25. 40 + 40 + 100 + 100 + 200 = 480 sq ft 8 ft 5 ft 10 ft 20 ft 20 ft 40 sq ft 100 sq ft 5 ft 8 ft 10 ft 20 ft 10 ft 200 sq ft 40 sq ft 100 sq ft

  26. Nets • A net is all the surfaces of a rectangular solid laid out flat. Back 8 cm 5 cm Top Right Side lt. Side Top 8 cm Side Front 8 cm Front 8 cm 5 cm 10 cm Bottom 5 cm 10 cm

  27. Find the Surface Area using nets. Top Back 8 cm 80 Side Front 40 40 8 cm Left Side Top Right Side 50 5 cm 5 cm 8 cm 10 cm Front 8 cm 80 Each surface is a rectangle. A = lw 50 5 cm Bottom 10 cm Find the area of each surface. Which surfaces are the same? Find the Total Surface Area. 50+80+50+80+40+40 340 cm2

  28. Your Turn A = s2 A = 72 A = 49 in2 7 in S.A. = 49(6) S.A. = 294 in2

  29. Your Turn • Surface area word problems: • Bob is wrapping a present that is 12 inches long, 4 inches wide, and 3 inches tall. What is the minimum amount of wrapping paper required? F 4x3 = 12 12 + 12 + 48 + 48 + 36 + 36 = 192 in² B 4x3 = 12 T 12 x 4 = 48 3 Bt 12 x 4 = 48 LS = 12 x 3 = 36 RS = 12 x 3 = 36 12 4

  30. Your Turn Find the surface area of the triangular prism. 10 ft 8 ft 22 ft 15 ft

  31. 8 ft 10 ft 15 ft 22 ft 22 ft 10 ft 8 ft 15 ft 22 ft 15 ft

  32. 8 ft 10 ft 15 ft 22 ft 22 ft 60 sq ft 220 sq ft 10 ft 8 ft 15 ft 22 ft 15 ft 330 sq ft 60 sq ft 220 sq ft

  33. 60 + 60 + 220 + 220 + 330 = 890 sq ft 8 ft 10 ft 15 ft 22 ft 22 ft 40 sq ft 100 sq ft 10 ft 8 ft 15 ft 22 ft 15 ft 200 sq ft 40 sq ft 100 sq ft

  34. I can… • Determine the surface area of rectangular prisms • Determine the surface area of triangular prisms Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

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