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= a√15 cubic units. Find the value of a

Algebra ->  Polygons -> 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= a√15 cubic units. Find the value of a       Log On


   

Question 1198243: 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
Answer by ikleyn(52884) About Me  (Show Source):
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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
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Find the area of the triangular base. Use the Heron's formula.


The half of the perimeter of the base triangle is  s = %2812%2B14%2B16%29%2F2 = 42%2F2 = 21.


The area of the base is  A = sqrt%2821%2A%2821-12%29%2A%2821-14%29%2A%2821-16%29%29 = sqrt%2821%2A9%2A7%2A5%29 = 7%2A3%2Asqrt%2815%29 = 21%2Asqrt%2815%29.


The volume of the pyramid is  %281%2F3%29%2AA%2A22 = %281%2F3%29%2A21%2A22%2Asqrt%2815%29 = 7%2A22%2Asqrt%2815%29 = 154%2Asqrt%2815%29.


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.