# geometry

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A right pentagonal prism is 10 cm high. If the area of each pentagonal base is 32 cm squared and the perimeter is 20 cm, what are the lateral and total surface areas of the prism?

I tried doing this using the formula shown in my book, but it came out wrong. the formula I was using was for a triangular prism. What the heck is the formula for a pentagonal prism?

• geometry -
• geometry -

triangular prism ---> base is a triangle
pentagonal prism ---> base is a pentagon

So clearly you can't use the triangular prism formula for this question , but you an generalize it looking what it describes.

I don't know what they gave you, but the surface area of a triangular prism consists of
2 congruent triangular bases + 3 congruent rectangles

so the surface area of a pentagon
= 2 (area of the pentagon) + 5rectangles

you are given that the perimeter is 20, so each side of the base is 20/5 = 4, and the height is 10
so the surface area of the 5 rectangles is 5(4)(10) = 200
add the 2 pentagon areas of 32 each for a total of

200 + 64 = 264 cm^2

your text should give you the definitions of lateral and total surface areas, make the necessary adjustments.

• geometry -

Thank you, that makes more sense than what I tried.

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