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Answer: A=5t2 /4 (tan 54)

Explanation

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The base of a pentagonal prism is a pentagon. To find that area, we start with the general area of a regular polygon. Let abe the apothem and P be the perimeter of the polygon. The area, A=1/2Pa

Now let t be the length of any side of the pentagon and substitute in for the apothem and we have:

A=1/2 x 5t x t/2(tan 54)

or A=5t2 /4 (tan 54)

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