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mckenzieandjesus

  • one year ago

Find the area of the equilateral triangle. 4m square root ft2 12 squart root ft2 2 square root ft2 6mc053-4.jpg ft2

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  1. mckenzieandjesus
    • one year ago
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  2. mckenzieandjesus
    • one year ago
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    @jim_thompson5910

  3. mckenzieandjesus
    • one year ago
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    oops here Find the area of the equilateral triangle. 4 square root 3 ft2 12 square root 3 ft2 2 square root 3 ft2 6 square root 3 ft2

  4. jim_thompson5910
    • one year ago
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    I'm guessing that point is the circumcenter and the length of 4 is the circumradius.

  5. jim_thompson5910
    • one year ago
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    |dw:1435281664406:dw|

  6. mckenzieandjesus
    • one year ago
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    ok

  7. jim_thompson5910
    • one year ago
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    draw in the other circumradii |dw:1435281712679:dw|

  8. jim_thompson5910
    • one year ago
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    each central angle is 360/3 = 120 degrees |dw:1435281776974:dw|

  9. jim_thompson5910
    • one year ago
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    and since we have an isosceles triangle |dw:1435281812412:dw|

  10. jim_thompson5910
    • one year ago
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    we know that these angles here |dw:1435281843370:dw| are 30 degrees each (solve x+x+120 = 180 for x to get x = 30)

  11. anonymous
    • one year ago
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    are you deriving the formula for the length of the side?

  12. jim_thompson5910
    • one year ago
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    break up the triangle into two pieces we will have a 30-60-90 triangle |dw:1435281907823:dw|

  13. jim_thompson5910
    • one year ago
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    I'm showing how to find the length of each side. Then we can use the formula \[\Large A = \frac{\sqrt{3}}{4}s^2\]

  14. anonymous
    • one year ago
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    oh i see

  15. mckenzieandjesus
    • one year ago
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    whats s?

  16. jim_thompson5910
    • one year ago
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    it's the length of each side of the equilateral triangle |dw:1435281897863:dw|

  17. mckenzieandjesus
    • one year ago
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    oh ok. so square root 3/4*4^2?

  18. jim_thompson5910
    • one year ago
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    s = 4 is false

  19. mckenzieandjesus
    • one year ago
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    ohh

  20. jim_thompson5910
    • one year ago
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    all of these drawings are building up to find s

  21. Mertsj
    • one year ago
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    |dw:1435281547572:dw|

  22. jim_thompson5910
    • one year ago
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    |dw:1435282026879:dw|

  23. mckenzieandjesus
    • one year ago
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    oh ok

  24. jim_thompson5910
    • one year ago
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    |dw:1435282090401:dw| what are x and y?

  25. mckenzieandjesus
    • one year ago
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    4?

  26. jim_thompson5910
    • one year ago
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    have a look at this page http://www.regentsprep.org/regents/math/algtrig/att2/ltri30.htm

  27. jim_thompson5910
    • one year ago
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    notice how the short leg (opposite the 30 degree angle) is half of the hypotenuse

  28. mckenzieandjesus
    • one year ago
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    2 and 1?

  29. jim_thompson5910
    • one year ago
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    close |dw:1435282277842:dw|

  30. jim_thompson5910
    • one year ago
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    long leg = sqrt(3) times (short leg)

  31. mckenzieandjesus
    • one year ago
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    ohh

  32. mckenzieandjesus
    • one year ago
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    ohh i see

  33. jim_thompson5910
    • one year ago
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    the long leg is exactly half of s so that's why s = 2*(2*sqrt(3)) = 4*sqrt(3)

  34. mckenzieandjesus
    • one year ago
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    ah ok

  35. jim_thompson5910
    • one year ago
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    |dw:1435282367672:dw|

  36. mckenzieandjesus
    • one year ago
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    okay

  37. mckenzieandjesus
    • one year ago
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    So the answer is 4 square root 3 then. Not 12 square root 3

  38. jim_thompson5910
    • one year ago
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    \[\Large s = 4\sqrt{3}\] |dw:1435282458289:dw|

  39. jim_thompson5910
    • one year ago
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    they want the area, NOT the side length

  40. mckenzieandjesus
    • one year ago
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    ohh oops

  41. jim_thompson5910
    • one year ago
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    plug that s value into the area formula \[\Large A = \frac{\sqrt{3}}{4}s^2\]

  42. Mertsj
    • one year ago
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    |dw:1435282443589:dw|

  43. Mertsj
    • one year ago
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    The triangle is divided into 3 congruent triangles.

  44. Mertsj
    • one year ago
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    Consider one of the triangles.

  45. mckenzieandjesus
    • one year ago
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    so \[A = \frac{ \sqrt{3} }{ 4? } * S ^{2}\]

  46. mckenzieandjesus
    • one year ago
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    oops ment to put 4 square root 3 for s

  47. Mertsj
    • one year ago
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    |dw:1435282544885:dw|

  48. mckenzieandjesus
    • one year ago
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    So would I put 4 square root 3 for s?

  49. Mertsj
    • one year ago
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    The area of that triangle is 1/2 base x height or \[\frac{1}{2}\times 4\sqrt{3}\times 2=4\sqrt{3}\]

  50. Mertsj
    • one year ago
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    Since there are three of those triangles, multiply that answer by 3

  51. mckenzieandjesus
    • one year ago
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    oh okay i added and got 12 square root 3

  52. mckenzieandjesus
    • one year ago
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    I guess it works either way lol thanku

  53. Mertsj
    • one year ago
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    And that is the answer.

  54. Mertsj
    • one year ago
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    Do you understand now?

  55. mckenzieandjesus
    • one year ago
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    Yes I do

  56. mckenzieandjesus
    • one year ago
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    Is the formula of a rectangle A=bh?

  57. Mertsj
    • one year ago
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    yes

  58. mckenzieandjesus
    • one year ago
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    or is it A= 1/2 bh?

  59. Mertsj
    • one year ago
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    A=bh

  60. mckenzieandjesus
    • one year ago
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    oh ok

  61. mckenzieandjesus
    • one year ago
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    thanku!

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