for the square pyramid, the lateral edge length, e, is 25 in, and the slant height, s, is 24 in. Find the height of the pyramid, h. Round the answer to the nearest whole number.
To find the height of the square pyramid, we can use the Pythagorean theorem. The slant height (s) is the hypotenuse of a right triangle formed by the height (h) and half the lateral edge length (e/2).
Using the Pythagorean theorem:
s² = (e/2)² + h²
24² = (25/2)² + h²
576 = 625/4 + h²
576 = 156.25 + h²
576 - 156.25 = h²
419.75 = h²
Taking the square root of both sides:
√419.75 = √h²
20.49 ≈ h
Therefore, the height of the pyramid is approximately 20 inches.