SOLUTION: The length of the base of a square pyramid is 12 inches. Given that the surface area of the square pyramid is 336 square inches, find the height of the pyramid.

Algebra ->  Pythagorean-theorem -> SOLUTION: The length of the base of a square pyramid is 12 inches. Given that the surface area of the square pyramid is 336 square inches, find the height of the pyramid.      Log On


   

Question 1134786: The length of the base of a square pyramid is 12 inches. Given that the surface area of the square pyramid is 336 square inches, find the height of the pyramid.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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            The solution by  @josgarithmetic  is   a b s o l u t e l y   w r o n g   and   t o t a l l y   i r r e l e v a n t.

            For your safety simply ignore it.

            I came to bring the correct solution - see below. 


1.  First, the lateral surface area of the given pyramid is  336+-+12%5E2 = 336 - 144 = 192 square inches.


2.  The lateral surface area consists of 4 congruent triangles - so the area of each triangle is  192%2F4 = 48 square inches.


3.  The base of each such a triangle is 12 inches; hence, the slant height of the pyramid is  %2848%2F12%29%2A2 = 8 inches.


4.  Then the height of the pyramid is  sqrt%288%5E2-%2812%2F2%29%5E2%29 = sqrt%288%5E2-6%5E2%29 = sqrt%2864+-+36%29 = sqrt%2828%29 = 2%2Asqrt%287%29 units.    ANSWER

Solved.