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)
To apply the Pythagorean theorem, we need to identify the right triangle formed by the height line (h), the slant height (25 feet), and the distance from the center of the base to the vertex.
The base edge length is given as 40 feet. This means the distance from the center of the base to the vertex is half of that, which is 20 feet.
Using the Pythagorean theorem, we have:
(height)^2 + (base)^2 = (slant height)^2
Replacing the variables with their values, we get:
(h)^2 + (20 feet)^2 = (25 feet)^2
Simplifying, we have:
h^2 + 400 = 625
Subtracting 400 from both sides, we get:
h^2 = 225
Taking the square root of both sides, we get:
h = √225
h = 15 feet
Therefore, the height of the square pyramid is approximately 15 feet.