one formula for the area of a regular polygon is:

Area = (1/2)(apothem)(perimeter)

we are given the apothem, the perimeter is just the length of all the sides.

let A be the apothem, and P be the permeter.

then A = 3

and P = 6*2sqrt(3) = 12sqrt(3)

so we have,

Area = (1/2)AP

.......= (1/2)*3*12sqrt(3) cm^2

.......= 18sqrt(3) cm^2

see Area of a Regular Polygon and Regular polygon area formula for more info