Question

The lateral area of a pyramid with a square base is 1,080 sq. ft. Its base edges are 18 ft. long. How do you find the height of the pyramid?

Answer 1

The height of the pyramid is `28.62` ft.

Explanation:

We know lateral surface area `(A_l)` of square base right pyramid as
`A_l = a * sqrt (a^2+4h^2)` where `a` is the base edge and `h` is the height of pyramid.

`A_l =1080 , a= 18 , h = ? ; :. 1080 = 18*sqrt (18^2+4h^2) or sqrt (18^2+4h^2)=1080/18=60`Squaring both sides we get ,

`60^2= (18^2+4h^2) or 4*h^2 =3600 -324 = 3276 or h^2 =3276/4=819 :. h = sqrt 819 or h ~~ 28.62 (2dp) ft`

The height of the pyramid is `28.62` ft. [Ans]