SOLUTION: A regular hexagonal pyramid has one lateral edge which measures 10 cm. The length of one side of its base is 6 cm. Find the altitude and the slant height of the given pyramid.

Question 1087628: A regular hexagonal pyramid has one lateral edge which measures 10 cm. The length of one side of its base is 6 cm. Find the altitude and the slant height of the given pyramid.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
A regular hexagon can be seen as made of 6 equilateral triangle "slices".
The base of that pyramid can be seen as this:

A vertical cross-section of that pyramid
(cutting through the apex and base vertices and center of the base of the pyramid)
would look like this
The Pythagorean theorem says that ,
so the altitude of the pyramid measures .
The triangles that form the sides of the pyramid}} are isosceles triangles with 6 cm bases and 10 cm sides.
Their altitude is the slant height of the pyramid,
and it can also be calculated, using the Pythagorean theorem, as

.
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