Question 1198261
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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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<pre>
Find the area of the triangular base. Use the Heron's formula.


The half of the perimeter of the base triangle is  s = {{{(12+14+16)/2}}} = {{{42/2}}} = 21.


The area of the base is  A = {{{sqrt(21*(21-12)*(21-14)*(21-16))}}} = {{{sqrt(21*9*7*5)}}} = {{{7*3*sqrt(15)}}} = {{{21*sqrt(15)}}}.


The volume of the pyramid is  {{{(1/3)*A*22}}} = {{{(1/3)*21*22*sqrt(15)}}} = {{{7*22*sqrt(15)}}} = {{{154*sqrt(15)}}}.


Thus a = 154.    <U>ANSWER</U>
</pre>

Solved.



On the Heron's formula, &nbsp;see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Surface-area/-Proof-of-the-Heron%27s-formula-for-the-area-of-a-triangle.lesson>Proof of the Heron's formula for the area of a triangle</A>  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Surface-area/One-more-proof-of-the-Heron%27s-formula-for-the-area-of-a-triangle.lesson>One more proof of the Heron's formula for the area of a triangle</A>  

in this site.