Question

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

Answer 1

It's a square pyramid, and its height is unknown, and the slant height is 25 feet, and the length is 40 feet. Remember that the height is right in the middle of the square pyramid, creating a right triangle

Answer 2

I don't have the diagram or which lengths are given, so I need one more detail to pick the correct answer: which two measurements are given in the problem (for example, the base side length and the slant height, or the base side and the edge length, or the distance from apex to a corner, etc.)? Or please paste the problem text or an image.

How you'll use the Pythagorean Theorem (choose the case that matches your diagram):

- If you are given the slant height l (distance from the apex to the midpoint of a side) and the base side length s, then the right triangle has legs h and s/2 and hypotenuse l, so
h = sqrt(l^2 − (s/2)^2).

- If you are given the lateral edge length e (distance from the apex to a corner) and the base side length s, then the right triangle has legs h and (half the base diagonal) = s·√2 / 2, and hypotenuse e, so
h = sqrt(e^2 − (s·√2/2)^2).

Tell me which measurements correspond to which parts (or paste the figure), and I will compute h and choose the correct option (31.2, 15.0, 32.0, or 47.2 ft) rounded to the nearest tenth.