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)

Answer 1

To find the height of the pyramid, h, we first need to find the length of the slant height of the lateral face, r.

Using the Pythagorean theorem, we can find r:
r^2 = s^2 - (0.5e)^2
r^2 = 24^2 - (0.5 * 25)^2
r^2 = 576 - 156.25
r^2 = 419.75
r ≈ √419.75
r ≈ 20.48

Now that we have r, we can find the height, h, by using the Pythagorean theorem again:
h^2 = s^2 - r^2
h^2 = 24^2 - 20.48^2
h^2 = 576 - 419.75
h^2 = 156.25
h = √156.25
h ≈ 12.5

Therefore, the height of the pyramid is approximately 12 inches.

Answer 2

The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth.

Answer 3

To find the length of the edge of the square base of the pyramid, we first need to find the length of the diagonal of the square base, which is also the slant height, s.

Given:
Height (h) = 321 ft
Slant Height (s) = 436.5 ft

To find the length of the diagonal (d) of the square base, we can use the Pythagorean theorem in 2 dimensions:

d^2 = s^2 + s^2
d^2 = 2s^2
d = √(2s^2)
d = √(2 * 436.5^2)
d = √(2 * 190380.25)
d = √380760.5
d ≈ 617.2 ft

Since the diagonal (d) of the square base is equal to the length of the edge multiplied by √2, we have:

Edge Length (e) = d / √2
Edge Length (e) = 617.2 / √2
Edge Length (e) ≈ 435.7 ft

Therefore, the length of the edge of the square base of The Pyramid in Memphis, Tennessee is approximately 435.7 ft.