Question 867352
The altitude forms two right triangles, congruent to each other, and the height is one of the legs.  One leg is half of 6 or 3; and the hypotenuse is 11.  Height? 

Let height be y.
Pythagorean Theorem:  {{{3^3+y^2=11^2}}}.
Take the rest....




{{{y=sqrt(121-9)=sqrt(112)=sqrt(28*4)=sqrt(4*4*7)}}}
{{{y=4*sqrt(7)}}}