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osanseviero

  • one year ago

Problem. You have an equilateral triangle (side l) with 3 circles inside of r=1. I need to calculate the area of the triangle (without the circle area)

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  1. osanseviero
    • one year ago
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  2. madhu.mukherjee.946
    • one year ago
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    find the area of the circle

  3. madhu.mukherjee.946
    • one year ago
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    what do you get?

  4. osanseviero
    • one year ago
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    pi*r^2

  5. madhu.mukherjee.946
    • one year ago
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    so whats the area of the circle putting the radius

  6. osanseviero
    • one year ago
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    pi

  7. madhu.mukherjee.946
    • one year ago
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    so whats the area for 3 circles

  8. osanseviero
    • one year ago
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    A = 3pi

  9. madhu.mukherjee.946
    • one year ago
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    now find the area of the equilatral triangle as a whole,whats that

  10. madhu.mukherjee.946
    • one year ago
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    do you know the formula to find the area of equi triangle

  11. madhu.mukherjee.946
    • one year ago
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    @osanseviero

  12. osanseviero
    • one year ago
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    I'm working to get the formula, almost there

  13. madhu.mukherjee.946
    • one year ago
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    this is the formula

  14. madhu.mukherjee.946
    • one year ago
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    A=root3/4a^2

  15. madhu.mukherjee.946
    • one year ago
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    @osanseviero now you got it?

  16. osanseviero
    • one year ago
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    So sqrt(3)*l^2 / 4

  17. osanseviero
    • one year ago
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    Just got it :)

  18. madhu.mukherjee.946
    • one year ago
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    |dw:1441337140712:dw|

  19. madhu.mukherjee.946
    • one year ago
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    this is the formula

  20. madhu.mukherjee.946
    • one year ago
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    now at the place of a^2 you will put l^2 as side of the triangle is l

  21. osanseviero
    • one year ago
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    So At = \[At = \frac{l ^{2} \sqrt{3} }{ 4 } -3\pi\]

  22. madhu.mukherjee.946
    • one year ago
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    exactly

  23. beginnersmind
    • one year ago
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    You can get an exact numeric answer. My terrible drawing shows how you can slice up the triangle into pieces that can be calculated exactly. |dw:1441336935522:dw|

  24. madhu.mukherjee.946
    • one year ago
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    nice drawing:)

  25. beginnersmind
    • one year ago
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    Well, that's assuming that the 3 circles are tangent to each other and the sides of the triangle.

  26. osanseviero
    • one year ago
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    They are

  27. osanseviero
    • one year ago
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    So how could I get a numeric answer?

  28. osanseviero
    • one year ago
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    Going to see this, thanks for the help https://www.youtube.com/watch?v=4lwhAfhRXXo

  29. beginnersmind
    • one year ago
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    There are three types of regions in my drawing, labelled P, Q and R. Can you find the area of either? (hint Q is a rectangle)

  30. beginnersmind
    • one year ago
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    The top region is P of course, not Q. Anyway, added a couple of hints about some angles and lines. |dw:1441337851708:dw|

  31. beginnersmind
    • one year ago
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    Anyway, the best idea would be to calculate l, then go from there.|dw:1441338129100:dw| This should be the simplest solution.

  32. osanseviero
    • one year ago
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    Ok. So I got that the side is l = 2r +2rsqrt(3). Since r is 1: l = 2 + 2sqrt(3)

  33. beginnersmind
    • one year ago
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    I got 2 + 4sqrt(3)

  34. beginnersmind
    • one year ago
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    sorry, that makes no sense. let me check

  35. beginnersmind
    • one year ago
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    |dw:1441338549521:dw| Yeah, 2+2sqrt(3) is correct.

  36. beginnersmind
    • one year ago
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    |dw:1441338637803:dw|

  37. osanseviero
    • one year ago
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    So the final area is around 3.5?

  38. beginnersmind
    • one year ago
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    Can you finish the rest? (hint use pythagoras to get the altitude and don't forget to subtract the area of the circles)

  39. beginnersmind
    • one year ago
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    let me check real quick

  40. beginnersmind
    • one year ago
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    Yeah, I got 3.504

  41. osanseviero
    • one year ago
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    Thanks!

  42. beginnersmind
    • one year ago
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    Cool. Sorry for leading you down the wrong path at first :)

  43. osanseviero
    • one year ago
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    No problem, thanks a lot for all the help

  44. beginnersmind
    • one year ago
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    No problem.

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