Question

If the side length of the base of a square pyramid is divided by 4 and the slant height is divided by 3, what is the surface area formula that represents these changes?
a) SA = n(1/8 lb) + 1/16 B
b) SA = n(1/24 lb) + 1/16 B
c) SA = n(1/24 lb) + ¼ B
d) SA = n(1/12 lb) + ¼ B

Answer 1

SA = area of the base  + area of one face * 4

area of the base = [base side] ^2

area of a face = (base side * slant height/2)

new base side = original base side / 4

new slant height = original slant height / 3

new area of the base = [base side / 4]^2 = [base side]^2 / 16

new area of a face =[base side / 4][slant height / 3] = [base side][slant height] / 12

area of the four faces = 4*  [base side][slant height] / 12

 
SA = [base side]^2 / 16 +  4*[base side][slant height] / 12 =

=  [base side]^2 / 16 +  4*[base side][slant height / 2] / 12 =

=  [base side]^2 / 16 +  4*[base side][slant height] / 24

Then if n = number of faces of the pyramid, B = area of the  base, and lb is base side * slant height

SA = B/16 + n(lb/24), which is option b)