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anonymous

  • one year ago

Describe a method you can use to find the area of the following shape. Provide specific details in your answer, including coordinates and descriptions of shapes used. Then, find the actual area of the figure.

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    @zepdrix

  3. anonymous
    • one year ago
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    @ganeshie8

  4. zepdrix
    • one year ago
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    Hey :) So umm.. how bout break it up into some more manageable shapes?

  5. anonymous
    • one year ago
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    okay, how should we start doing that?

  6. zepdrix
    • one year ago
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    |dw:1440473225733:dw|

  7. anonymous
    • one year ago
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    Are we wanting to divide it into 3 shapes or just however many we can make ?

  8. zepdrix
    • one year ago
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    Well I'm thinking like this maybe:|dw:1440473387371:dw|because rectangles and right triangles are really easy to deal with :)

  9. zepdrix
    • one year ago
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    Do you understand how to find the coordinates of each point?

  10. zepdrix
    • one year ago
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    Or rather I should say: Do you understand how to use the coordinates to find the side lengths?

  11. anonymous
    • one year ago
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    Okay(: So what is our first step? sorry im really not good at this. I think so isn't that do you count like up and down along y axis and and left to right on x axis ?

  12. zepdrix
    • one year ago
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    `Provide specific details in your answer, including coordinates and descriptions of shapes used. Then, find the actual area of the figure.` Yes, counting the squares is a much better way of doing it, but it looks like they want us to include coordinates and all of that business :(

  13. anonymous
    • one year ago
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    ughh :( okay so then how do we do that ?

  14. zepdrix
    • one year ago
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    |dw:1440473666198:dw|Do you understand how I came up with these two coordinates?

  15. anonymous
    • one year ago
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    For B you counted up 8 and counted left 11 units For C you counted left 11 units but the zero you didnt move at all ?

  16. zepdrix
    • one year ago
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    Yes, those distances. But your 'directions' seem backwards lol :) For B you count 8DOWN and 11RIGHT. We're starting from the point (0,0) and going towards B. I think you did it the other way around.

  17. zepdrix
    • one year ago
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    Oh boy this is gonna be tricky... I wonder if there is a simpler way we can chop this up...

  18. anonymous
    • one year ago
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    Oh your right i did my bad lol(: Hmmm could we do AC and that be a right triangle ? would that be an easier way to chop it up ?

  19. zepdrix
    • one year ago
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    |dw:1440474034288:dw|Hmm prolly not :) that leaves us with a nasty shape here

  20. zepdrix
    • one year ago
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    Are you comfortable with trapezoids?

  21. zepdrix
    • one year ago
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    |dw:1440474081780:dw|Cause maybe this would be easier

  22. anonymous
    • one year ago
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    kinda , im deffinetly gonna need help though

  23. anonymous
    • one year ago
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    So does that mean what we did with B and C earlier...forget that ?

  24. zepdrix
    • one year ago
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    It'll end up saving us some steps since we don't have to find all these little shapes in the middle. Just three now. To find the area of a trapezoid, we multiply the base length by the average of the side/height lengths.\[\large\rm A=b\cdot\frac{h_1+h_2}{2}\] How long is side BC?

  25. anonymous
    • one year ago
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    I thought 11 units , correct?

  26. zepdrix
    • one year ago
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    |dw:1440474292576:dw|I'm just gonna label all of the points that we'll need.

  27. zepdrix
    • one year ago
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    |dw:1440474388966:dw|

  28. zepdrix
    • one year ago
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    from 0 down to -8

  29. anonymous
    • one year ago
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    so would the height be -8 and 0 for BC

  30. zepdrix
    • one year ago
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    The height is the distance from 0 to -8. That ends up being a distance of 8 if you count the boxes, ya?

  31. anonymous
    • one year ago
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    Yes your right, im just trying to plug in the h1 and h2 too quick lol sorry

  32. zepdrix
    • one year ago
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    |dw:1440474556848:dw|How bout from D down the bottom? You're at -3 and you're going down to -8, how many boxes between those?

  33. zepdrix
    • one year ago
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    Make sure you're using the original image :) Mine kinda stinks since you can't count the boxes lol

  34. anonymous
    • one year ago
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    Okay(: Would that be 5?

  35. zepdrix
    • one year ago
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    |dw:1440474733035:dw|Good :O Then the base? Looks like we're going from x=6 over to x=11

  36. anonymous
    • one year ago
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    would the base be 6?

  37. zepdrix
    • one year ago
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    We're going from 6 to 11. You can do subtraction if you feel more comfortable with that. 11-6 = 5 So a length of 5 across the bottom.

  38. anonymous
    • one year ago
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    Okay i must have counted wrong, so now i plug in the numbers?

  39. zepdrix
    • one year ago
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    \[\large\rm A=b\cdot\frac{h_1+h_2}{2}\qquad\to\qquad A_1=5\cdot\frac{5+8}{2}\]Plug all the information in! :) What do we get for the area of our first shape? Yah sorry I stole some of the fun there, just trying to move this along hehe.

  40. anonymous
    • one year ago
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    Haha its okay(: so then it would be 13/2 = 6.5 then 6.5 X5 = 32.5 SO would our answer be 32.5?

  41. zepdrix
    • one year ago
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    |dw:1440475130927:dw|Ok great! We're 1/3 done lol

  42. anonymous
    • one year ago
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    Great(: ! So now do we do the same thing to the other shape ?

  43. zepdrix
    • one year ago
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    Let's ignore the coordinates for now. Just use those in your explanation maybe :p|dw:1440475216912:dw|

  44. zepdrix
    • one year ago
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    Yes, let's work on this trapezoid in the bottom left here. Can you figure out the side lengths by counting the boxes?

  45. anonymous
    • one year ago
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    That would be 2 if your counting up and if your counting left then that would be 5

  46. zepdrix
    • one year ago
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    Hmm 5 doesn't sound quite right.

  47. anonymous
    • one year ago
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    Then im confused i counted to the F and it was 5 units

  48. zepdrix
    • one year ago
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    |dw:1440475453452:dw|

  49. anonymous
    • one year ago
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    Oh i see my mistake, i moissed one, my bad :/

  50. zepdrix
    • one year ago
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    So we have our information again, good. \(\large\rm h_1=1,\quad h_2=6,\quad b=2\) plug it in to find the area of your second shape.

  51. anonymous
    • one year ago
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    One question first, how did you get the 1?

  52. anonymous
    • one year ago
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    A = 7?

  53. zepdrix
    • one year ago
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    |dw:1440475703801:dw|

  54. zepdrix
    • one year ago
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    So that length is 1 from 5 to 6, ya? :o

  55. anonymous
    • one year ago
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    Oh yeah your right , duhhh(: so my answer would be 7 correct ?

  56. zepdrix
    • one year ago
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    |dw:1440475843531:dw|Mmmmmm k good. let's try to figure out this last one. Luckily we have a free side already! Since this trapezoid shares a side with the bottom one, we know that the long edge is still 6.

  57. zepdrix
    • one year ago
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    What about the other lengths? :o

  58. anonymous
    • one year ago
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    well from D to E that would be 2

  59. anonymous
    • one year ago
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    the other length would be 3

  60. zepdrix
    • one year ago
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    |dw:1440476101788:dw|Ok good! :)

  61. anonymous
    • one year ago
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    h1 = 3 h2 = 6 b=2?

  62. zepdrix
    • one year ago
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    The h's should be across from one another.

  63. anonymous
    • one year ago
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    b= 3 and h2= 2

  64. anonymous
    • one year ago
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    Im sorry , for the confusion im just trying to understand .. so the answer would be 12?

  65. zepdrix
    • one year ago
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    |dw:1440476358788:dw|Good. And the total area would be the sum of those three areas. \(\large\rm A=A_1+A_2+A_3\)