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Math Help - pyramid....

  1. #1
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    Cool pyramid....

    1.) Find the lateral area of a regular hexagonal pyramid if each edge of base is 10m and each lateral edge is 15m.

    2.) Find the volume and the lateral area of a regular triangular pyramid if the altitude is 20 inches and the base of equal sides is 9 inches.

    3.) Find the volume and the total area of a triangular pyramid if each lateral edge is 30 meters and the base is 10 meters on a side. It's base is an equilateral triangle.
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, orochimaru700!

    Here's the first one . . .


    1) Find the lateral area of a regular hexagonal pyramid
    . . .if each edge of base is 10m and each lateral edge is 15m.
    I assume the "lateral edge" is what most of us call the "slant height".


    One of the triangular side panels looks like this:
    Code:
                  *
                 /|\
                / | \
               /  |  \ 15
              /  h|   \
             /    |    \
            /     |     \
           /      |      \
          * - - - * - - - *
                      5

    From Pythagorus: . h^2 + 5^2 \:=\:15^2 \quad\Rightarrow\quad h^2 \:=\:200 \quad\Rightarrow\quad h \:=\:10\sqrt{2}

    The area of this triangle is: . \tfrac{1}{2}bh \:=\:\tfrac{1}{2}(10)\left(10\sqrt{2}\right) \:=\:50\sqrt{2}\text6{ m}^2


    Therefore, the area of the six panels is: . A \;=\;6\times 50\sqrt{2} \;=\;300\sqrt{2}\text{ m}^2

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