Question

Use the image to answer the question.

An illustration shows a square pyramid with labeled parts. The left, front, and right faces of the pyramid and base are visible. The back face is not visible, but its position is indicated by a dashed line. The back base edge is not visible, but its position is indicated by a dashed line. The left base edge is labeled a. The back left lateral edge is labeled e. A dotted line extends from the interior of the vertex straight down to the center of the base and is labeled h. A right angle is indicated where the dotted height line meets the base. Another dotted line extends from the center of the base where the height line meets to the center of the right base edge and is labeled r. A dotted line extends from the right base edge straight up the center of the right face of the prism and meets the height line at the vertex. The dotted slant height line is labeled s.

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
.

(1 point)
The height of the square pyramid is
___ in.

expialn bot

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

Since r is the distance from the center of the base to the center of the right base edge, we can use the Pythagorean theorem to find its length.

We know that the lateral edge length, e, is 25 in. and the slant height, s, is 24 in.

Using the Pythagorean theorem, we have:

r^2 + s^2 = e^2

r^2 + 24^2 = 25^2

r^2 + 576 = 625

r^2 = 625 - 576

r^2 = 49

Taking the square root of both sides, we find:

r = √49

r = 7

Now that we know the length of r, we can find the height, h.

Looking at the illustration, we can see that the height, h, is the distance from the vertex to the center of the base, along the dotted line.

Since the slant height, s, is the distance from the vertex to the center of the right face, we can use the Pythagorean theorem again to find h.

Using the Pythagorean theorem, we have:

h^2 + r^2 = s^2

h^2 + 7^2 = 24^2

h^2 + 49 = 576

h^2 = 576 - 49

h^2 = 527

Taking the square root of both sides, we find:

h = √527

h ≈ 22

Therefore, the height of the square pyramid is approximately 22 in.