[tex] \alpha = 60 \\ \tan( \alpha ) = \tan(60) = \sqrt{3} \\ \tan( \alpha ) = \frac{8 \sqrt{3} }{AD} \\ \sqrt{3} = \frac{8 \sqrt{3} }{AD} \\ AD = 24 \\ AC = AD + DC = 24 + 4 = 28 \\ S_{ABC} = \frac{1}{2} AC \times BD = \frac{1}{2} \times 28 \times 8 \sqrt{3} = 112 \sqrt{3} [/tex]