Question 727386
The base 30-60-90 triangle is half of an equilateral triangle, so using L for the unknown long leg of this triangle, {{{L^2+15^2=30^2}}}.  The 15 is half a side of the equilateral triangle giving us the given base triangle.

{{{L=sqrt(30^2-15^2)}}} comes from the just given equation.  Now, area of this base triangle is {{{(1/2)15sqrt(30^2-15^2)}}}.  The prism is 100 cm high, so the volume of this prism is then {{{(1/2)*100*15sqrt(30^2-15^2)}}} cm^2.


With simplification, volume may be shown as {{{750sqrt(675)=11250sqrt(3)}}}.