SOLUTION: The lateral area of a pyramid with a square base is 2400in^2. Its base edges are 48in long. Find the height of the pyramid.

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Question 965140: The lateral area of a pyramid with a square base is 2400in^2. Its base edges are 48in long. Find the height of the pyramid.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
lateral area/4=area of one side =1/2(base edge)(slant height)
2400in%5E2%2F4=%281%2F2%29bs
600in%5E2=%281%2F2%29%2848in%29%28s%29
600in%5E2=%2824in%29s
25in=s The slant height is 25 inches.
The height and 1/2 the base length form a right triangle with the slant height as hypotenuse, so:
s%5E2=%28b%2F2%29%5E2%2Bh%5E2 where h is the height
%2825in%29%5E2=%2824in%29%5E2%2Bh%5E2
%2825in%29%5E2-%2824in%29%5E2=h%5E2
sqrt%28%28625in%5E2%29-%28576in%5E2%29%29=h
sqrt%2849in%5E2%29=h
7in=h ANSWER: The height of the pyramid is 7 inches.