question_answer

The\[x-\]axis, y-axis and a line passing through the point A(6, 0) form a\[\Delta ABC\]. If\[\angle A=30{}^\circ ,\] then the area of the triangle (in sq unit) is

A)  \[6\sqrt{3}\]         

B)  \[12\sqrt{3}\]

C)  \[4\sqrt{3}\]        

D)  \[8\sqrt{3}\]

Correct Answer: A

Solution :

In \[\Delta AOB,\]    \[\tan 30{}^\circ =\frac{OB}{OA}\] \[\Rightarrow \] \[\frac{1}{\sqrt{2}}=\frac{OB}{6}\] \[\Rightarrow \] \[OB=\frac{6\sqrt{3}}{3}\] \[=2\sqrt{3}\] \[\therefore \]Area of \[\Delta AOB=\frac{1}{2}\times OA\times OB\] \[=\frac{1}{2}\times 6\times 2\sqrt{3}\] \[=6\sqrt{3}\]sq units