A stainless steel patio heater is a square pyramid. The length of one side of the base is 24.8 in. The slant height of the pyramid is 93.5 in. What is the height of the pyramid?

The height of the pyramid is 92.67 inches

Step-by-step explanation:

Here, we are interested in calculating the perpendicular height of the pyramid given the slant height of the pyramid.

Now, let's say that the side of the square is a, half of this length is r and the slant height is represented by s.

Mathematically, from Pythagoras' theorem, we know that the square of the hypotenuse equals the sum of the square of the two other sides.

With the hypotenuse being the slant height s,

s^2 = r^2 + h^2

but r is just half of the length of the side of the square base = a/2 = 24.8/2 = 12.4 inches

93.5^2 = 12.4^2 + h^2

h^2 = 93.5^2 - 12.4^2

h^2 = 8742.25 - 153.76

h^2 = 8,588.49

h = √ (8,588.49)

h = 92.67 inches