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?

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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?

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Answer 1 · 2017-05-11T11:09:12

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]

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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?

1 Answer

Explanation:

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