Pyramid problem

**olokish** · January 26th 2010, 04:27 AM

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.?

**earboth** · January 26th 2010, 07:58 AM

Originally Posted by olokish

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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