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

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)

Ithink it’s b, hope this .

Ithink it is correct but just ask someone else but i am sure it it