Question

A stainless steel patio heater is a square pyramid the length of one side of the base is 23.2 in the slant height of the pyramid is 90.5 in what is the height of the pyramid

Answer 1

To find the height of the square pyramid, you can use the Pythagorean theorem because the slant height, base length, and height of the pyramid form a right triangle.

Let:
- Base length (a) = 23.2 inches
- Slant height (c) = 90.5 inches

We can use the Pythagorean theorem:

a^2 + h^2 = c^2

Where:
- a is the base length
- h is the height
- c is the slant height

Now, plug in the values:

(23.2)^2 + h^2 = (90.5)^2

Solve for h:

h^2 = (90.5)^2 - (23.2)^2
h^2 = 8202.25 - 538.24
h^2 = 7664.01

Now, take the square root of both sides to find h:

h = √7664.01
h ≈ 87.6 inches

So, the height of the square pyramid is approximately 87.6 inches.