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. Hint: Before finding the length of h
, you will first need to find the length of r
.
(1 point)
The height of the square pyramid is
in.
To find the height of the square pyramid, first we need to find the length of the slant height.
Using the Pythagorean theorem, we can find the length of the base of the pyramid.
Let's denote the height of the pyramid as h, and the side length of the base as b.
We can form a right triangle with the slant height (s), half the base (b/2), and the height (h) of the triangle.
Using the Pythagorean theorem, we have:
(s)^2 = (b/2)^2 + (h)^2
Plugging in the given values, we have:
(24 in)^2 = (b/2)^2 + (h)^2
576 in^2 = (b/2)^2 + (h)^2
Since it is a square pyramid, the base is a square and all sides are equal. Therefore, b = b/2 * 2, where 2 is the side length of the base.
Simplifying the equation, we have:
576 in^2 = (2b/2)^2 + (h)^2
576 in^2 = b^2 + (h)^2
Since we are given that the lateral edge length is 25 in, the base length (b) must also be 25 in.
Plugging in the value for b, we have:
576 in^2 = (25 in)^2 + (h)^2
576 in^2 = 625 in^2 + (h)^2
(h)^2 = 576 in^2 - 625 in^2
(h)^2 = -49 in^2
Since the square of a real number cannot be negative, we have no real solution for (h)^2, which means we cannot find the height of the pyramid.