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.

Algebra ->  Formulas -> 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.       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
First let's draw the pyramid (note: my drawings are not to scale).

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If we just look at the base, we get something like this (Note: The hypotenuse was found through pythagorean's theorem sqrt%286%5E2%2B6%5E2%29=sqrt%2836%2B36%29=sqrt%2872%29=6%2Asqrt%282%29):

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Now take half of the hypotenuse to get 3%2Asqrt%282%29. This figure will form the leg of the triangle. Now let's one half of a triangular cross section to get this:

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From the drawing, we can see that legs are h and 3%2Asqrt%282%29 while the hypotenuse is 6


So to find "h", we need to use pythagorean's theorem:

a%5E2%2Bb%5E2=c%5E2


h%5E2%2B%283%2Asqrt%282%29%29%5E2=6%5E2 Plug in a=h, b=3%2Asqrt%282%29, and c=6


h%5E2%2B%283%2Asqrt%282%29%29%5E2=36 Square 6 to get 36.


h%5E2%2B18=36 Square 3%2Asqrt%282%29 to get


h%5E2=36-18 Subtract 18 from both sides.


h%5E2=18 Combine like terms on the right side.


h=sqrt%2818%29 Take the square root of both sides. Note: only the positive square root is considered.


h=3%2Asqrt%282%29 Simplify.


So the height is h=3%2Asqrt%282%29 or h=4.24264


So the height of the pyramid to the nearest hundredth of an inch is 4.25 inches