Question

a stainless steel patio heaters a square pyramid. The length of one side of the base is 24.6 in the slant height of the pyramid is 91.8 inches what is the height of the pyramid?

Answer 1

For a square pyramid, its height, slant height, and base form a right triangle:

Where

a is the length of one side of the base

r is the inner radius of the base (and is equal to half the length of a side of the base)

h is the height

s is the slant height

To determine the height (h) you can apply the Pythagorean theorem that states that the square of the hypothenuse is equal to the sum of the squares of the sides of the right triangle:

`s^2=h^2+r^2`

Write the expression for the height:

`\begin{gathered} h^2=s^2-r^2 \\ h=\sqrt[]{s^2-r^2} \end{gathered}`

For

s= 91.8inch

r=a/2=24.6/2=12.3in

Replace these values in the expression obtained for h

`\begin{gathered} h=\sqrt[]{s^2-r^2} \\ h=\sqrt[]{(91.8^2)-(12.3^2)} \\ h=\sqrt[]{8275.95} \\ h=90.97 \end{gathered}`

The height of the pyramid is 90.97inches.