Question

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.

15.0 ft.
15.0 ft.

32.0 ft.
32.0 ft.

47.2 ft.
47.2 ft.

Answer 1

To determine the height \( h \) of a square pyramid using the Pythagorean Theorem, we need to know the lengths of the base and the slant height of the pyramid.

Assuming we have a square pyramid with base side length \( a \) and slant height \( l \), the relationship can be defined as:

1. The height \( h \), half of the base length \( \frac{a}{2} \), and the slant height \( l \) form a right triangle.
2. By the Pythagorean theorem:

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

From which we can solve for the height \( h \):

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

Please provide the dimensions (the side length of the base and the slant height) so we can calculate the height \( h \) and round the answer to the nearest tenth. If those values are not provided, we cannot proceed with calculating the height.