Question 578514
{{{drawing(300,150,-7.5,7.5,-2,5.5,
triangle(-6.928,0,6.928,0,0,4),
red(line(0,0,0,4)), locate(-0.5,3.7,120^o),
locate(0.1,2,h=4),locate(3.5,2.6,8), locate(-4,2.6,8),
locate(-5.8,1.2,30^o)
)}}} The triangle is split by the altitude into two 30-60-90 right triangles.
The sides of the right triangles measure 4, 8, and {{{4sqrt(3)}}}
The base of the isosceles triangle measures {{{8sqrt(3)}}}
The area of the isosceles triangle is {{{(1/2)*(8sqrt(3))*(4)=16sqrt(3)}}}