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.

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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) About Me  (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 red%28H%29%5E2%2Bgreen%286cm%29%5E2=%2810cm%29%5E2 ,
so the altitude of the pyramid measures red%28H%29=sqrt%28%2810cm%29%5E2-green%286cm%29%5E2%29=highlight%288cm%29 .
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 s of the pyramid,
and it can also be calculated, using the Pythagorean theorem, as
s%5E2%2B%283cm%29%5E2=%2810cm%29%5E2
s%5E2%2B9cm%5E2=100cm%5E2
s%5E2=100cm%5E2-9cm%5E2
s%5E2=91cm%5E2
s=highlight%28sqrt%2891%29%29cm=abouthighlight%289.54cm%29 .