SOLUTION: The base edges of a triangular pyramid are 12, 14, and 16, and its altitude is 22. The volume of the pyramid may be expressed as V = α√15 cubic units. Find the value of α.

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Question 1198261: The base edges of a triangular pyramid are 12, 14, and 16, and its altitude is 22.
The volume of the pyramid may be expressed as V = α√15 cubic units. Find the value of α.
Answer by ikleyn(52898)   (Show Source): You can put this solution on YOUR website!
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The base edges of a triangular pyramid are 12, 14, and 16, and its altitude is 22.
The volume of the pyramid may be expressed as V= a√15 cubic units. Find the value of a
~~~~~~~~~~~~~~~ 

Find the area of the triangular base. Use the Heron's formula.


The half of the perimeter of the base triangle is  s =  =  = 21.


The area of the base is  A =  =  =  = .


The volume of the pyramid is   =  =  = .


Thus a = 154.    ANSWER

Solved.


On the Heron's formula,  see the lessons
    - Proof of the Heron's formula for the area of a triangle
    - One more proof of the Heron's formula for the area of a triangle
in this site.



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