Question

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

23 in.

Answer 2

To find the height of the pyramid, we first need to find the length of the radius of the base.

The radius of the base of a square pyramid is equal to half of the length of one side of the base. Since the lateral edge length is 25 inches, the length of one side of the base is also 25 inches. Therefore, the radius of the base is 25/2 = 12.5 inches.

Now, we can use the Pythagorean theorem to find the height of the pyramid. The height, slant height, and radius form a right triangle. The slant height is the hypotenuse of this triangle, the height is one of the legs, and the radius is the other leg.

Using the Pythagorean theorem, we have:

h^2 + r^2 = s^2

Substituting the known values, we get:

h^2 + 12.5^2 = 24^2

h^2 + 156.25 = 576

h^2 = 576 - 156.25

h^2 = 419.75

Taking the square root of both sides, we find:

h = √419.75

h ≈ 20.5

Therefore, the height of the pyramid is approximately 20.5 inches, rounding to the nearest whole number, it is 21 inches.