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, you will first need to find the length of r
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To find the height of the pyramid, we first need to find the length of r, which is the distance from the center of the base to the apex (top) of the pyramid.
In a square pyramid, the slant height (s) is the hypotenuse of a right triangle, with the lateral edge length (e) as one leg and the height (h) as the other leg.
Using the Pythagorean theorem, we can find the length of r.
s^2 = e^2 + h^2
24^2 = 25^2 + h^2
576 = 625 + h^2
h^2 = 576 - 625
h^2 = -49
Since the square root of a negative number is not a real number, this means there is no real height for the pyramid.