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
31.2 ft.
31.2 ft.
15.0 ft.
15.0 ft.
32.0 ft.
32.0 ft.
47.2 ft.
47.2 ft.
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page 15 of 15
To determine the height of the square pyramid, we can use the Pythagorean Theorem which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the right triangle is formed by the slant height, the height, and the base edge.
The slant height is given as 25 feet and the base edge is given as 40 feet.
Using the Pythagorean Theorem:
(25^2) = (h^2) + (40^2)
625 = h^2 + 1600
625 = h^2 + 1600
h^2 = 1600 - 625
h^2 = 975
Taking the square root of both sides:
h ≈ 31.2 ft
Therefore, the height of the square pyramid is approximately 31.2 feet.