Find the slant height for the pyramid below. The base length is 16 and the height is 24.
We cannot find the slant height with only the given information. We need to know either the angle between the base and a slant height, or the length of one of the triangular faces of the pyramid.
To find the slant height of a pyramid, we can use the Pythagorean Theorem. The slant height is the hypotenuse of a right triangle formed by the height, the slant height, and half the base length.
Let's call the slant height "s" and the height "h". We know that the base length is 16. Therefore, half the base length is 16/2 = 8.
Using the Pythagorean Theorem, we can set up the equation:
s^2 = h^2 + (8)^2.
Plugging in the values we have, we get:
s^2 = (24)^2 + (8)^2.
Simplifying, we have:
s^2 = 576 + 64.
s^2 = 640.
Taking the square root of both sides, we find:
s = √640.
We can simplify the square root of 640:
s ≈ √(64 × 10) = √64 × √10 = 8√10.
Therefore, the slant height of the pyramid is approximately 8√10.