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unearthly09 Group Title

What is the surface area of this three-dimensional, symmetrical, capital letter “I” block? Show your work.

  • 2 years ago
  • 2 years ago

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  1. unearthly09 Group Title
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    • 2 years ago
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  2. dpflan Group Title
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    All right, how familiar with surface area are you?

    • 2 years ago
  3. unearthly09 Group Title
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    i know how to find the surface area of rectangular prisms just need a little help with the composite figurs

    • 2 years ago
  4. dpflan Group Title
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    We need to determine the number of sides, or specific planes, that the 'I' has. Like a cube, a cube has 6 sides that are in the shape of squares. This 'I' has quite a 'sides'. So, we'll want to find the area of all these different sides and sum them.

    • 2 years ago
  5. unearthly09 Group Title
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    why the area?

    • 2 years ago
  6. dpflan Group Title
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    Cool, can you determine the number of sides?|dw:1343144067033:dw|

    • 2 years ago
  7. dpflan Group Title
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    Surface area is just the sum of all the area of the outside of this 3D object. That is the surface, the part you can touch if you were actually holding the 'I', so surface area just means you find the area of the surface, or the outside skin if you will of the object

    • 2 years ago
  8. unearthly09 Group Title
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    oh i get it

    • 2 years ago
  9. dpflan Group Title
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    So perhaps the best way to go about this would be to look at the 'I' straight on. If you can imagine that you have this object and can rotate, this will be simple ;)

    • 2 years ago
  10. dpflan Group Title
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    |dw:1343144255358:dw|

    • 2 years ago
  11. unearthly09 Group Title
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    ok

    • 2 years ago
  12. dpflan Group Title
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    The best part is that this 'I' is symmetric, so it it has the same properties from different view points. so if we view only the front of the 'I'|dw:1343144361875:dw| this is what the back looks like too

    • 2 years ago
  13. unearthly09 Group Title
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    yeah

    • 2 years ago
  14. dpflan Group Title
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    You are given the lengths of all the sides. So, what would be the area of just the front ?

    • 2 years ago
  15. unearthly09 Group Title
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    what do u mean the area of the I

    • 2 years ago
  16. dpflan Group Title
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    Find the area of the three rectangles that make up the front. Like how I drew the front, even though the attached picture has the front being one large shape of a capital I, you could break that shape down into smaller shapes: like 2 big rectangles at the top and a square in the middle

    • 2 years ago
  17. unearthly09 Group Title
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    would it be 22cm

    • 2 years ago
  18. dpflan Group Title
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    Yeah, nice! So that takes care of the front, well, and the back areas.

    • 2 years ago
  19. dpflan Group Title
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    area of front + area of back + area of left side + area of right side + area of top + area of bottom

    • 2 years ago
  20. dpflan Group Title
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    Due to the symmetry, we can just find the area of the front (=area of back), area of right side (=area of left), and the area of the top (=area of bottom)

    • 2 years ago
  21. dpflan Group Title
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    Now the side is more difficult, it is more complex than the front.

    • 2 years ago
  22. dpflan Group Title
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    How many rectangles comprise a side of the surface?

    • 2 years ago
  23. unearthly09 Group Title
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    is it 3 the 3 long ones and the one short one

    • 2 years ago
  24. unearthly09 Group Title
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    i meant 2 long ones

    • 2 years ago
  25. dpflan Group Title
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    |dw:1343144879045:dw| The black diagonal lines are for the left side, which we want to work with

    • 2 years ago
  26. unearthly09 Group Title
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    i have a question is the answer 104???

    • 2 years ago
  27. dpflan Group Title
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    Heh, cut the chase, eh? Just a second

    • 2 years ago
  28. unearthly09 Group Title
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    ha:D

    • 2 years ago
  29. dpflan Group Title
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    No, that's not big enough

    • 2 years ago
  30. dpflan Group Title
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    ...

    • 2 years ago
  31. unearthly09 Group Title
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    so where did i go wrong i have no clue what I did

    • 2 years ago
  32. dpflan Group Title
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    Heh, I'm checking my math...

    • 2 years ago
  33. dpflan Group Title
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    because I messed up, 104 is right

    • 2 years ago
  34. unearthly09 Group Title
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    really!!!!

    • 2 years ago
  35. dpflan Group Title
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    5 squares for the left side surface, each 2x2 = 20 2 long rectangles, 5x2, and 1 small square, 2x1 for the front = 22 1 long rectangle, 5x2, for the top = 10 That is 52, so due to symmetry, 52x2 is the total surface area

    • 2 years ago
  36. dpflan Group Title
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    Yes, how did you get it? If you wrote down your work,you can take a picture of it with maybe your cell phone and upload your work on here

    • 2 years ago
  37. unearthly09 Group Title
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    i really kind of did what u told me than i found the area of the 2 sides

    • 2 years ago
  38. unearthly09 Group Title
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    my work is all jumbled up

    • 2 years ago
  39. dpflan Group Title
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    Oh well, very cool though, that's a straightforward way to solve it, so nice work!

    • 2 years ago
  40. unearthly09 Group Title
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    does this make sense symmetrical, capital letter i I would find the surface area of one of the "bars" 5 by 2 by 2 (ignoring the fact that the middle connector hides part of the surface). So one bar has 4 sides with 5 by 2 or 4*10= 40 sq cm the 2 ends have area 2*2=4 or 8 total. So the bar has a surface area of 48 Double this for the other bar: 96 Now the middle connector has 4 sides. I used 2 of them to "fill in" the hidden part of the bar We have 2 sides of 2x2 or 2 sides of 4 or 8 sq cm to add in 96 8 104 Therefore the surface area of this figure is 104 centimeters squared.

    • 2 years ago
  41. unearthly09 Group Title
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    i meant 96+8= 104

    • 2 years ago
  42. dpflan Group Title
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    The middle part however has 2 2x1 sides, and 2 2x2 sides that are visible, and 2 2x1 sides that not visible, if you break the 'I' in 3 3D objects: 2 prisms on the top, 1 in the middle

    • 2 years ago
  43. unearthly09 Group Title
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    yeah

    • 2 years ago
  44. unearthly09 Group Title
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    right...???

    • 2 years ago
  45. dpflan Group Title
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    Usually, if you are going to include a part, such as the under side of the top block, which is not part of the 'I''s surface area, that means you need to actually subtract that amount of 'hidden surface area' from the final total.

    • 2 years ago
  46. dpflan Group Title
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    Let's see: 3 blocks: 2 long rectangles and 1 middle connector

    • 2 years ago
  47. dpflan Group Title
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    the long rectangles are similar, so let's just focus on one: We are going to use your concept of building the 'I' from these 3 objects and accounting for hidden area. So, the surface area of one long block is: 4 - 5x2 rectangles 2 - 2x2 rectangles SA = 4(10) + 2(4) = 48 So surface area of both blocks is 48x2 = 96 Now, the middle connector: 2 - 2x2 rectangles 4 - 2x1 rectangles SA = 2(4) + 4(2) = 16 But 2 of those 2x1 rectangles are hidden once all the blocks are connected And, in each long block, an area of 2x1 is hidden too. 96 + 16 - 4(2x1) = 112 - 8 = 104

    • 2 years ago
  48. dpflan Group Title
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    |dw:1343146032157:dw| In the 2 circled parts, we have to account for the hidden parts of the surface when the blocks are all connected. So we you quite close, and I think you're idea of working with the 3 blocks is a little more intuitive

    • 2 years ago
  49. dpflan Group Title
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    Does this make sense?

    • 2 years ago
  50. unearthly09 Group Title
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    yes it does....thank u so much :)

    • 2 years ago
  51. dpflan Group Title
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    No problem, I think you can do your other questions if they're similar, you seem to have the right intuition about how to solve the problem

    • 2 years ago
  52. unearthly09 Group Title
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    :)thanks again

    • 2 years ago
  53. unearthly09 Group Title
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    bye

    • 2 years ago
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