For the square pyramid the lateral edge length is 25in and the slant height is 24 in. Find the height of the pyramid
To find the height of the square pyramid, we can use the Pythagorean Theorem.
We know that the slant height is 24 inches and the lateral edge length is 25 inches. Let's call the height of the pyramid "h".
The lateral edge length of the square base forms a right triangle with the slant height and the height of the pyramid. The height of the pyramid is the vertical leg of this right triangle.
Using the Pythagorean Theorem, we have:
h² + 12² = 24²
Simplifying the equation:
h² + 144 = 576
Subtracting 144 from both sides of the equation:
h² = 432
Taking the square root of both sides:
h = √432 ≈ 20.784
So, the height of the pyramid is approximately 20.784 inches.