Find the slant height, showing all steps of your work. Leave your answer in simplest radical form.

Question

Find the slant height, showing all steps of your work. Leave your answer in simplest radical form.

Answer 1

Draw in the slant height as a perpendicular to the middle of a side on the base.

The slant height is a leg of a right triangle where the other leg is half the length of the side of the base (3) and the hypotenuse is the length of the edge (6)

Based on the Pythagorean Theorem:

slant height ** 2 + 3^2 = 6^2

slant height ** 2 = 9 = 36

slant height ** 2 = 27

slant height = 3 sqrt(3)