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# Square prism and square pyramid

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A square prism and square pyramid have the same base and the smae surface area. Show that the slant height, l, of the pyramid is l= (5/2)s where s is the length of the base.

May 6, 2018
edited by Guest  May 7, 2018

#1
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I'm pretty sure it is unanswerable with that limited info, but I am rusty on this topic.

May 6, 2018
#2
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There's nothing wrong with the question, there is sufficient information, look at it again.

May 6, 2018
#3
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SA of square pyramid =[Base Area] + 1/2 × Perimeter × [Slant Length ]      SA of square prism = 2 × Base Area + Base Perimeter × Length

Let the base area of both = S^2
The perimeter of both =4S
S^2 + [1/2*4S] * L = [2 * S^2] + 4S*S , solve for L=Slant Height
2 L S + S^2 = 6 S^2

Subtract S^2 from both sides:
2 L S = 5 S^2

Divide both sides by 2 S:
L = 5/2S - Slant Length[Height] of the pyramid.

May 6, 2018
#4
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In your equation you assumed that the length of the square prism is equal to s (the side of the base), isn't correct as if these lines were equal then the shape would be a cube rather than a square prism, nonetheless using my differing aprroach doesn't give an answer, so I assume the question wasn't written properly, as you need to assume the square prism is a cube to solve for l.

Shonk  May 6, 2018