In a certain regular square pyramid, all of the edges have length $12$. Find the volume of the pyramid.
Find the height of the pyramid to be sqrt 108 (use pythag theorem)
volume = 1/3 (12)(12) (sqrt(108)) units3
sqrt (3) / 2 = slant height / 12
6sqrt (3) = sqrt (108) = slant height
Height = sqrt (108 - 36) = sqrt (72) = 6sqrt (2)
Volume =
(1/3) 12^2 * 6 sqrt (2) =
288 sqrt (2) units^3
+37157 
