Question 389139
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Hi,         
'regular square pyramid' with base edge length 12 and the altitude of 8
<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/9/91/Pyramid.svg/200px-Pyramid.svg.png">
surface area = base area + area of the 4 faces(lateral area)
Area of trangular face = (1/2)b*slant height
Picture drawing an altitude from the apex to the base, forming right triangle
using the Pythagoream Theorem c^2 = a^2 = b^2 where c is the slant height
slant height for this 'square pyaramid' = {{{sqrt( 8^2 + 6^2) = sqrt(100) = 10}}}
lateral area = 4 [(1/2)12*10) = 2*120 = 240
surface area =  base area + 180 = 12*12 + 240 = 144 + 240 = 384