Question 173197
Area of the base is {{{pi * r^2}}}
Area of the cone is pi * r * s, where r is the radius and s the distance from the apex of the cone to the base. 

The area of the whole figure then is A = {{{pi * r^2  + pi * r * s}}}


You are given the value of r, but not of s. You can calculate though because it is the hypotenuse of a right triangle with s and h as its legs. From the Pythagorean theorem, {{{a^2 + b^2 = c^2}}}


{{{6^2 + (6sqrt(3))^2 = s^2}}}
{{{36 + 36*3 = s^2}}}
{{{144 = s^2}}}
s = 12


Substitute the values of s and r in the above equation to calculate the area

A = {{{pi * r^2  + pi * r * s}}}

If you factor the Pi from both terms:
A = {{{Pi * (r^2 + rs)}}}
A = {{{Pi (6^2 + 6*12)}}}
A = {{{Pi (108)}}}
A = 339.28 sq cm