For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number. Hint: Before finding the length of h , you will first need to find the length of r The height of the square pyramid is?

Answer 1

To solve this problem, we can use the Pythagorean Theorem.

Let's consider one of the triangular faces of the pyramid. We can see that the side length of the base is the same as the lateral edge length e, which is 25 inches.

Let r be the height of one of the triangles (which is also the height of the pyramid).

Using the Pythagorean Theorem, we can find r:

r^2 + (e/2)^2 = s^2

r^2 + (25/2)^2 = 24^2

r^2 + 12.5^2 = 576

r^2 + 156.25 = 576

r^2 = 576 - 156.25

r^2 = 419.75

r ≈ √419.75

r ≈ 20.49

Now that we have the height of the triangle (r), we can use it to find the height of the pyramid. Since the height of the pyramid is the same as the height of the triangular faces, the height of the pyramid is approximately 20 inches.