To find the slant height of the square pyramid, we can use the Pythagorean theorem.
The base of the pyramid is a square, so the length of one side of the square base is 16 feet.
The height of the pyramid is given as 15 feet, and the slant height is the hypotenuse of a right triangle formed by the height and one half of the base.
Using the Pythagorean theorem, we can find the slant height:
slant height^2 = height^2 + (1/2 x base)^2
slant height^2 = 15^2 + (1/2 x 16)^2
slant height^2 = 225 + 64
slant height^2 = 289
Taking the square root of both sides to find the slant height:
slant height = √289
slant height = 17 feet
Therefore, the slant height of the square pyramid is 17 feet.
Triangles Unit Test
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Question
Use the image to answer the question.
An illustration shows a square pyramid with labeled parts. The front and left faces of the pyramid and base are visible. The back and right faces are not visible. The back and right base edges are not visible but their position is indicated by a dashed line. The left base edge shows a length of 16 feet. A dotted line extends from the interior of the vertex straight down to the center of the base and shows a height of 15. A right angle is indicated where the dotted height line meets the base.
Find the slant height of the square pyramid.
(1 point)
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