Since \triangle ABC is an equilateral triangle, the height h and the sides of the triangle makes a 30-60-90 special right angle triangle \triangle BCD . The ratio of the triangle is 1:\sqrt{3} :2.

Therefore,

DB = \dfrac{1}{2}BS = 3

h = CD = \sqrt{3} BD = 3\sqrt{3}

According to the area formula of a triangle,

S_{\triangle ABC } = \dfrac{1}{2}AB \cdot h = \dfrac{1}{2}\cdot 6\cdot 3\sqrt{3} = 9\sqrt{3}