The Pythagorean Theorem in Three Dimensions Quick Check
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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
32.0 ft.
32.0 ft.
31.2 ft.
31.2 ft.
47.2 ft.
47.2 ft.
15.0 ft.
To find the height (h) of the square pyramid, you can use the Pythagorean Theorem.
The base of the pyramid forms a right triangle with the height (h) as the hypotenuse. The base edges are half of 40 feet, so each base edge is 20 feet. The slant height is given as 25 feet.
Using the Pythagorean Theorem:
(20)^2 + h^2 = (25)^2
400 + h^2 = 625
h^2 = 225
h = √225
h = 15 feet
Therefore, the height of the square pyramid is 15 feet.
The correct answer is: 15.0 ft.