Question

Find the slant height of the square pyramid. (1 point)

Answer 1

The slant height of a square pyramid can be found using the Pythagorean Theorem.

Let the base of the pyramid be a square with side length s. Draw a right triangle from the center of the base to one of the vertices of the base. The hypotenuse of this right triangle is the slant height of the pyramid.

The hypotenuse of the right triangle is the diagonal of the base square. Since the base square is a square with side length s, the diagonal can be found using the Pythagorean Theorem:

diagonal^2 = s^2 + s^2
diagonal^2 = 2s^2

Therefore, the diagonal (or slant height) of the pyramid is the square root of 2 times the side length s:

diagonal = √(2s^2) = s√2.

So, the slant height of the square pyramid is s√2.