Question

A stainless steel patio heater is a square pyramid. The length of one side is 20.6 in. The slant height of the pyramid is 91.1 in. What is the height of the pyramid?

Answer 1

We know that the side L of the base of the pyramid is 20.6 in.

We also know that the slant height S is 91.1 in.

We have to find the height of the pyramid.

We can draw a cut of the pyramid, as if we were seeing it from one of the faces:

Then, we can apply the Pythagorean theorem to find H:

`\begin{gathered} H^2+((L)/(2))^2=S^2 \\ H^2=S^2-((L)/(2))^2 \\ H^2=91.1^2-((20.6)/(2))^2 \\ H^2=8299.21-11.3^2 \\ H^2=8299.21-127.69 \\ H^2=8171.52 \\ H=\sqrt[]{8171.52} \\ H\approx90.4 \end{gathered}`

Answer: The height of the pyramid is 90.4 in.