The pyramid shown has a square base that is 18 inches on each side. it has a surface area of 864 square inches. what is the slant height?

Answer:
the slant height is 15 inches.



let s be the slant height

surface area of a square base pyramid is

    sa = area base + 4 * (area of slant triangle)

the area of a slant triangle is 1/2 * (base length) * (slant height)  so

    sa = area base + 4 · [ 1/2 *  (base length) · (slant height) ]
    sa = area base + 2 ·  (base length) · (slant height) 

the (area base) is equal to 18in · 18in = 324in²
the (base length) is given in the question as 18
the sa is equal to 864
we can use this information to solve for (slant height), s

    864 = 324 + 2 · 18 · (slant height) 
    540 = 2 ·  18 · (slant height) 
    540 = 36  · (slant height) 
    slant height = 15

the slant height is 15 inches.