What is the height of a right pyramid with a square base that has a base edge length of 24 feet and a slant height of 20 feet?

To find the height of a right pyramid with a square base, we can use the relationships between the base dimensions and the slant height. In this case:

• The length of each edge of the base ( extit{b}) = 24 feet
• The slant height ( extit{s}) = 20 feet
• We need to find the vertical height ( extit{h}) of the pyramid.

First, we determine the length of the half-base edge, which is half of the base edge length:

Half of Base Edge: b/2 = 24/2 = 12 feet

Next, we can form a right triangle with the height ( extit{h}), half of the base edge, and the slant height ( extit{s}). This can be visualized as follows:

Right Triangle Relationship:

Using the Pythagorean theorem:

s² = h² + (b/2)²

Substituting the known values:

20² = h² + 12²

Calculating the squares:

400 = h² + 144

Now, we can isolate extit{h²}:

h² = 400 – 144

h² = 256

Now take the square root to find extit{h}:

h = √256 = 16 feet

So, the height of the right pyramid is 16 feet.