Slant height on square pyramid

Question

square pyramid has surface area of 110 sq yards, length of base in 7 yards, what is slant height?

Answer 1

110 = 49+ 14sqr(49/4 +h2)

surface area = a^2 +2asqr(a^2/4 + h^2)

where a = base edge length and

h= vertical height

use that to find the slant height=s

construct a right triangle with s= slant height = hypotenuse

h= vertical height is the height of the right triangle

then use the edge =7 to fjnd the base of the right triangle

sqr(49/4 +h^2) = (110-49)/14 = 61/14

49/4 + h^2 = (61/14)^2

h^2 = (61/14)^2 -49/4

h = sqr((61/14)^2 -49/4)

s^2 = h^2 + b^2 where b=(7/2)sqr2

s^2 = (61/14)^2 -49/4 + (7/2)sqr2

calculator recommended