Hi,         

'regular square pyramid' with base edge length 12 and the altitude of 8



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' = 

lateral area = 4 [(1/2)12*10) = 2*120 = 240

surface area =  base area + 180 = 12*12 + 240 = 144 + 240 = 384 

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