Question

Apply the Pythagorean Theorem to determine the height of the square pyramid, h. Round the
answer to the nearest tenth.
(1 point)
15.0 ft.
31.2 ft.
47.2 ft.
32.0 ft.

Answer 1

To apply the Pythagorean Theorem to determine the height of a square pyramid, we typically need the length of the base edges and the slant height or the height of the pyramid itself. If we assume that the slant height \(l\) is given (which can represent the distance from the apex to the midpoint of a side of the base), and the distance from the center of the base to the midpoint of one of the edges is half the base length, we can set up our equation.

Assuming:
- \(h\) = height of the pyramid
- \(a\) = length of a side of the base
- \(l\) = slant height

The relationships can be set up as follows:

1. The distance from the center of the base (midpoint) to one of the corners of the base is \( \frac{a}{2} \).
2. The slant height forms a right triangle with the height and half the base length.

Using the Pythagorean theorem:

\[
l^2 = h^2 + \left(\frac{a}{2}\right)^2
\]

Without specific values for \(l\) or \(a\), it is not possible to perform any calculation or derive the height \(h\).

However, you provided multiple choice answers (15.0 ft, 31.2 ft, 47.2 ft, 32.0 ft). To select the correct height \(h\), please provide additional information such as the slant height or the length of the base sides of the pyramid.