How to find the Total Area in a Pentagonal Prism.
(The given question: 'Find the total area (in terms of K) of the prism. Place "K" last in your formula)

Question

How to find the Total Area in a Pentagonal Prism.
(The given question: 'Find the total area (in terms of K) of the prism. Place "K" last in your formula)

anonymous · Answer

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mathstudent55 · Answer

Look at the following drawing:

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mathstudent55 · Answer

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mathstudent55 · Answer

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mathstudent55 · Answer

The area of each triangle is base times height divided by 2.
The base of the triangle is the side of the pentagon.
Since there are 5 triangles, the area of the pentagons is
A = 5bh/2, but 5b = the perimeter of the pentagon.
Also the height of each triangle is apothem of the pentagon.
This means that the area of the pentagon is the perimeter of the pentagon times the apothem divided by 2.

anonymous · Answer

So then how do I figure out how to find the Apothem?

mathstudent55 · Answer

$A_{base} = \dfrac{perimeter \times apothem}{2} $

mathstudent55 · Answer

Look in your figure. The apothem is k.

mathstudent55 · Answer

The lateral are is simply the area of 5 congruent rectangular sides.

mathstudent55 · Answer

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