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Falling_In_Katt

  • one year ago

Find the lateral area the regular pyramid. L. A. =

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  1. Falling_In_Katt
    • one year ago
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  2. misssunshinexxoxo
    • one year ago
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    This is a very awesome tutorial http://www.virtualnerd.com/tutorials/?id=PreAlg_11_01_0031

  3. misssunshinexxoxo
    • one year ago
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    The lateral area of a regular pyramid is 1/2p*l where p is the perimeter of the base and l is the slant height. The lateral formula for a cone is also 1/2p*l where p is the perimeter (or in this case the circumference) of the base and l is the slant height. It can also be shown as pi*r*l, where r is the radius of the base, or 1/2pi*d*l, where d is the diameter of the radius of the base. However, note that this is only the lateral area formula for a right cone. There can be many formulas for the lateral area of an oblique cone. And what they mean when they say they want the answer in terms of pi is that they do not want you to do any process to it. They want the pi to be in the answer. For example, instead of multiplying 3*pi, the answer would instead be 3pi. Or instead of adding 3 + pi, the answer would actually be 3 + pi.

  4. misssunshinexxoxo
    • one year ago
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    If you'd like more help; please let me know. Truly feel that tutorial should shine some light

  5. Falling_In_Katt
    • one year ago
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    okay

  6. perl
    • one year ago
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    the base of that pyramid is a hexagon, and a hexagon is made up of 6 equilateral triangles

  7. perl
    • one year ago
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    If we use this formula 1/2p*L We know p = 6*6 We have to find the slant height L

  8. Falling_In_Katt
    • one year ago
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    Wouldn't the slant height be 8?

  9. perl
    • one year ago
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    8 is the altitude or height of the pyramid

  10. Falling_In_Katt
    • one year ago
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    Okay so how do I find the slant height?

  11. perl
    • one year ago
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    First let's identify the slant height L . I drew it in purple http://prntscr.com/7qqtha

  12. Falling_In_Katt
    • one year ago
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    okay

  13. perl
    • one year ago
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    to find L we can construct a right triangle

  14. perl
    • one year ago
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    http://prntscr.com/7qqvbz

  15. Falling_In_Katt
    • one year ago
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    okay

  16. perl
    • one year ago
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    we know the leg 8, that is given. the other leg we don't know

  17. Falling_In_Katt
    • one year ago
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    correct

  18. perl
    • one year ago
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    but that leg is the altitude for an equilateral triangle as shown here http://prntscr.com/7qqwob

  19. Falling_In_Katt
    • one year ago
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    okay

  20. perl
    • one year ago
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    and what do we know about equilateral triangles

  21. perl
    • one year ago
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    an equilateral triangle can be divided into two triangles of 30 60 90 degrees

  22. Falling_In_Katt
    • one year ago
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    yes

  23. perl
    • one year ago
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    the ratio of the sides of a 30 60 90 triangle is \( 1 : \sqrt 3 : 2 \)

  24. Falling_In_Katt
    • one year ago
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    okay

  25. perl
    • one year ago
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    |dw:1436461601747:dw|

  26. perl
    • one year ago
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    the height of this triangle is the leg we need

  27. Falling_In_Katt
    • one year ago
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    okay

  28. perl
    • one year ago
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    so we need 3 : h : 6 to have same ratio as 1 : sqrt(3) : 2

  29. perl
    • one year ago
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    3 : 3 √3 : 6 works

  30. perl
    • one year ago
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    if you divide through by 3, you get 1 : √3 : 2

  31. Falling_In_Katt
    • one year ago
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    Is 3 the height?

  32. perl
    • one year ago
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    3√3 is the height

  33. perl
    • one year ago
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    |dw:1436462137479:dw|

  34. Falling_In_Katt
    • one year ago
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    So I would do \[\frac{ 1 }{ 2 }(6*6)(3\sqrt{3})\]

  35. perl
    • one year ago
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    almost, now we have to L

  36. Falling_In_Katt
    • one year ago
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    oh okay

  37. perl
    • one year ago
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    http://prntscr.com/7qr6c4

  38. perl
    • one year ago
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    We can use pythagorean theorem to find L

  39. perl
    • one year ago
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    8^2 + ( 3 √ 3)^2 = L^2

  40. Falling_In_Katt
    • one year ago
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    91?

  41. perl
    • one year ago
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    correct, that would be L^2 take the square root of that

  42. perl
    • one year ago
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    L^2 = 91 L = sqrt(91)

  43. perl
    • one year ago
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    So the lateral area will be $$\Large \frac{ 1 }{ 2 }(6*6)(\sqrt{91})$$

  44. perl
    • one year ago
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    I hope that was clear.

  45. Falling_In_Katt
    • one year ago
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    Thank you!

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