A regular hexagon can be divided into six equilateral triangles. The side length of each triangle is equal to the radius of the circle.

Given that the diameter of the circle is 12cm, the radius (r) is calculated as:

\( r = \frac{d}{2} = \frac{12}{2} = 6cm \)

The area (A) of an equilateral triangle with side length a is given by the formula:

\( A = \frac{{a^2 \cdot \sqrt{3}}}{4} \)

Substituting a = r = 6cm into this formula gives:

\( A = \frac{{6^2 \cdot \sqrt{3}}}{4} = 9\sqrt{3} cm² \)

Since there are six such triangles in a hexagon, the total area of the hexagon is:

\( Area = 6 \cdot A = 6 \cdot 9\sqrt{3} cm² = 54\sqrt{3} cm² \)