To find the slant height of a square pyramid, you need to know the height of the pyramid and the length of one side of the base.
If the height of the pyramid is h and the length of one side of the base is s, the slant height can be found using the Pythagorean theorem.
The slant height (l) is the hypotenuse of a right triangle, where the height (h) is one of the legs and half of the diagonal of the base (d/2) is the other leg.
Using the Pythagorean theorem, we can write the equation:
l^2 = h^2 + (d/2)^2
Since it is a square pyramid, the diagonal of the base (d) can be found using the Pythagorean theorem as well:
d^2 = s^2 + s^2
Simplifying the equation, we get:
d^2 = 2s^2
Taking the square root of both sides, we get:
d = sqrt(2s^2)
Substituting this value back into the equation for the slant height, we have:
l^2 = h^2 + (sqrt(2s^2)/2)^2
Simplifying further, we get:
l^2 = h^2 + (2s^2)/4
l^2 = h^2 + s^2/2
Taking the square root of both sides, we finally get the formula for the slant height (l):
l = sqrt(h^2 + s^2/2)
Therefore, the slant height of the square pyramid is sqrt(h^2 + s^2/2).
Find the slant height of the square pyramid.
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