Question 1134786
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The solution by &nbsp;@josgarithmetic &nbsp;is &nbsp;&nbsp;<U>a b s o l u t e l y &nbsp;&nbsp;w r o n g</U>&nbsp;&nbsp; and &nbsp;&nbsp;<U>t o t a l l y &nbsp;&nbsp;i r r e l e v a n t</U>.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For your safety simply ignore it.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I came to bring the correct solution - see below.



<pre>
1.  First, the lateral surface area of the given pyramid is  {{{336 - 12^2}}} = 336 - 144 = 192 square inches.


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


3.  The base of each such a triangle is 12 inches; hence, the slant height of the pyramid is  {{{(48/12)*2}}} = 8 inches.


4.  Then the height of the pyramid is  {{{sqrt(8^2-(12/2)^2)}}} = {{{sqrt(8^2-6^2)}}} = {{{sqrt(64 - 36)}}} = {{{sqrt(28)}}} = {{{2*sqrt(7)}}} units.    <U>ANSWER</U>
</pre>

Solved.