A) \[\sqrt{3{{a}^{2}}}\]sq cm
B) \[3\sqrt{3}{{a}^{2}}\]sq cm
C) \[\frac{{{a}^{2}}}{3}\]sq cm
D) \[2\sqrt{a}\]sq cm
Correct Answer: B
Solution :
\[\sin 30{}^\circ \,=\,\frac{1}{2}\,=\,\frac{OD}{2a}\] \[OD=\frac{2a}{2}\,=\,a\] \[\frac{1}{3}(AD)=OD\] \[\Rightarrow \] \[AD=3OD=3a\] \[\,\sin 60{}^\circ =\frac{AD}{AB}\] \[\frac{\sqrt{3}}{2}=\frac{3a}{AB}\] \[AB=2\sqrt{3a}\] Side of triangle \[=\,2\sqrt{3a}\] Area of triangle \[=\frac{\sqrt{3}}{4}\times {{(side)}^{2}}\] \[=\frac{\sqrt{3}}{4}\times {{(2\sqrt{3}a)}^{2}}\] \[=\frac{\sqrt{3}}{4}\times 4\times 3{{a}^{2}}\] \[\,=3\sqrt{3}{{a}^{2}}sq\,\,cm\]You need to login to perform this action.
You will be redirected in
3 sec