Use the image to answer the question.

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)

Answer 1

To find the slant height of the square pyramid, we can use the right triangle formed by the height of the pyramid, half of the base length, and the slant height.

1. The height (h) of the pyramid is given as 15 feet.
2. The length of the base (l) is 16 feet, therefore half of the base length (which is the base of the right triangle) is \( \frac{l}{2} = \frac{16}{2} = 8 \) feet.

Now, we can use the Pythagorean theorem to find the slant height \( s \):

\[ s^2 = h^2 + \left(\frac{l}{2}\right)^2 \] \[ s^2 = 15^2 + 8^2 \] \[ s^2 = 225 + 64 \] \[ s^2 = 289 \] \[ s = \sqrt{289} = 17 \text{ feet} \]

Thus, the slant height of the square pyramid is 17 feet.

Answer 2

are you sure
it says units answer in units

Answer 3

Yes, I can clarify that for you. The slant height we've calculated for the square pyramid is indeed 17.

When presenting the final answer, you'll want to state it with the appropriate units. Since the measurements were provided in feet, the answer should be expressed in feet as well.

Thus, the slant height of the square pyramid is 17 feet.