The median of a triangle cannot be considered as a base of that triangle.
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in an isosceles triangle
Because it's perpencicular to its apex
Only one line of symmetry, it is the line that contains the median of the isosceles triangle (that passes through the vertex and perpendicular to the base).
Divide the base in half and draw the median from the apex. This median is also the altitude and so its length is the required height. Also, since it is the altitude, it forms a right angled triangle. Using Pythagoras on this triangle, the height is 9*sqrt(3)/2.
It is a triangle whose interior angles are 45, 45 and 90 degrees