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.
32.0 ft.
32.0 ft.
47.2 ft.
47.2 ft.
15.0 ft.
To apply the Pythagorean Theorem to determine the height of the square pyramid, we can use the following formula:
h^2 = a^2 + b^2
Where:
h = height of the pyramid
a = slant height
b = half of the base length
In the given illustration, the slant height (a) is 25 feet and half of the base length (b) is 20 feet (since the front base edge has a length of 40 feet, and half of that is 40/2 = 20 feet).
Substituting these values into the formula, we have:
h^2 = 25^2 + 20^2
h^2 = 625 + 400
h^2 = 1025
Taking the square root of both sides, we find:
h ≈ √1025
h ≈ 32.0 ft.
Therefore, the height of the square pyramid (h) is approximately 32.0 ft.