Question

Use the image to answer the question.

A pyramid frustum with labeled dimensions.

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.
Incorrect

Use the Pythagorean Theorem twice. The slant height and lateral edge will help you find r
. Then use that number to solve for h
.
Remaining Attempts : 2
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Answer 1

Let the half-side (distance from center to midpoint of a side) be r. Then
e^2 = h^2 + 2r^2 and s^2 = h^2 + r^2.
Subtract: e^2 − s^2 = r^2 = 25^2 − 24^2 = 625 − 576 = 49, so r = 7 in.
Now s^2 = h^2 + r^2 → 24^2 = h^2 + 7^2 → h^2 = 576 − 49 = 527, so h = √527 ≈ 23 in.

Answer: 23 in.