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. The back base edge is not visible but its position is indicated by a dashed line. The front base edge shows a length of 40 feet. 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. 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. This dotted line shows a slant height of 25 feet. 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. 15.0 ft. 15.0 ft. 31.2 ft. 31.2 ft. 32.0 ft. 32.0 ft. Skip to navigation

Answer 1

The height of the square pyramid, h, is approximately b. 15.0 feet. therefore, option b. 15.0 feet is correct.

Based on the Pythagorean Theorem, we can determine the height of the square pyramid, h, using the following formula:

h² = s² - (1/4)b²

where:

s is the slant height (25 feet)

b is the base edge (40 feet)

Plugging in the values:

h² = 25² - (1/4)40²

h² = 625 - 400

h² = 225

Taking the square root of both sides:

h = √225

h ≈ 15.0 feet (rounded to the nearest tenth)

Therefore, the height of the square pyramid, h, is approximately b. 15.0 feet.

Question

Given a square pyramid with a base edge of 40 feet and a slant height of 25 feet, what is the height of the pyramid (h) to the nearest tenth of a foot?(1 point) Responses

a. 47.2 ft.

b. 15.0 ft.

c. 31.2 ft.

d. 32.0 ft.