ADB is a 30-60-90 triangle:
Angle BAD = 30
Angle ABD = 60
Angle ADB = 90
Also, BDC is a 30-60-90 triangle:
Angle CBD = 30
Angle BCD = 60
Angle BDC = 90
In a 30-60-90 triangle, The ratio of 3 sides is x : \(\sqrt{3}\)x : 2x
i.e. opposite to 30 = x
opposite to 60 = \(\sqrt{3}\)x
opposite to 90 = 2x
Using the above property;
AB = 6\(\sqrt{3}\) and BC = 6
Therefore, Area of triangle ABC = \(\frac{1}{2}\) x 6\(\sqrt{3}\) x 6 = 18\(\sqrt{3}\)
Hence, option C
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I hope this helps!
Regards:
Karun Mendiratta
Founder and Quant Trainer
Prepster Education, Delhi, Indiahttps://www.instagram.com/prepster_education/