Question

Find the slant height of the square pyramid.

(1 point)

Answer 1

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).