find the slant height of a square pyramid
side length 16
height 15
how do i do it
To find the slant height of a square pyramid, you can use the Pythagorean theorem. The slant height (L) is the hypotenuse of a right triangle formed by the height (H) and half the diagonal of the base (d/2).
1. Find the length of the diagonal of the base:
In a square, the diagonal (d) is related to the side length (s) by the Pythagorean theorem: d = √(s^2 + s^2).
For this square pyramid, where the side length is 16, the diagonal (d) of the base can be found as:
d = √(16^2 + 16^2) = √(256 + 256) = √512 = 16√2.
2. Calculate half the diagonal of the base:
Since the length (d) of the diagonal of the square base is 16√2, half the diagonal (d/2) can be found as:
d/2 = (16√2) / 2 = 8√2.
3. Apply the Pythagorean theorem to find the slant height:
Using the height (H) of the pyramid (15) and half the diagonal of the base (8√2), the slant height (L) can be calculated as:
L = √(H^2 + (d/2)^2) = √(15^2 + (8√2)^2)
= √(225 + 64 * 2)
= √(225 + 128)
= √353.
Therefore, the slant height of the square pyramid is approximately √353 (approximately 18.79 units).