SOLUTION: 7. The altitude of a regular triangular pyramid is the segment connecting a vertex to the centroid of the opposite face. A regular triangular pyramid has edges of length 6 inches.
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Question 149171: 7. The altitude of a regular triangular pyramid is the segment connecting a vertex to the centroid of the opposite face. A regular triangular pyramid has edges of length 6 inches. How tall is such a pyramid, to the nearest hundredth of an inch?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First let's draw the pyramid (note: my drawings are not to scale).
If we just look at the base, we get something like this (Note: The hypotenuse was found through pythagorean's theorem ):
Now take half of the hypotenuse to get . This figure will form the leg of the triangle. Now let's one half of a triangular cross section to get this:
From the drawing, we can see that legs are and while the hypotenuse is
So to find "h", we need to use pythagorean's theorem:
Plug in , , and
Square 6 to get 36.
Square to get
Subtract from both sides.
Combine like terms on the right side.
Take the square root of both sides. Note: only the positive square root is considered.
Simplify.
So the height is or
So the height of the pyramid to the nearest hundredth of an inch is 4.25 inches
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