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    Exclamation Pyramid problem

    Find the lateral area of a life raft in the form of a regular pentagonal pyramid if the slant height is 17 ft. and one edge of the base is 15 ft. How many persons could be accommodated if a person occupies a space of 8.5 sq. ft.?
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  2. #2
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    Quote Originally Posted by olokish View Post
    Find the lateral area of a life raft in the form of a regular pentagonal pyramid if the slant height is 17 ft. and one edge of the base is 15 ft. How many persons could be accommodated if a person occupies a space of 8.5 sq. ft.?
    1. Draw a rough sketch.

    2. Let e denote the edge of the base, h_s the slant height.
    Calculate the radius r of the circumscribed circle:

    \dfrac{\tfrac12 e}{r} = \cos(36^\circ)

    3. The area of a regular pentagon consists of 5 isosceles triangles with the base e and the radius as the other legs.

    A_5=5 \cdot \frac12 \cdot e \cdot r \cdot \cos(36^\circ)

    Divide A_5 by 8.5 to answer the question.

    3. The lateral area consists of 5 isosceles triangles with the base e=15 and the height h_s = 17 '.
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