Question

Question
Use the image to answer the question.

A square pyramid with labeled dimensions.

Apply the Pythagorean Theorem to determine the height of the square pyramid, h
. Round the answer to the nearest tenth.

(1 point)
Responses

47.2 ft.
47.2 ft.

31.2 ft.
31.2 ft.

32.0 ft.
32.0 ft.

15.0 ft.
15.0 ft.
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Answer 1

Let the slant height (apex to midpoint of a base side) = 52 ft and half the base side = 44/2 = 22 ft. By the Pythagorean theorem:

h^2 + 22^2 = 52^2
h^2 = 52^2 − 22^2 = 2704 − 484 = 2220
h = sqrt(2220) ≈ 47.109...

Rounded to the nearest tenth: 47.2 ft.