A) \[\frac{{{a}^{2}}}{3}\]
B) \[\frac{{{a}^{2}}}{4}\]
C) \[\frac{{{a}^{2}}}{6}\]
D) \[\frac{{{a}^{2}}}{8}\]
Correct Answer: C
Solution :
Length of an equilateral triangle is \[a\frac{\sqrt{3}}{2}.\] |
\[\therefore \] Radius of incircle \[=\frac{a\sqrt{3}}{2}\times \frac{1}{3}=\frac{a}{2\sqrt{3}}\] |
\[\therefore \] Diameter of incircle \[=2\left( \frac{a}{2\sqrt{3}} \right)=\frac{a}{\sqrt{3}}\] |
Let side of a square be x. |
\[\therefore \] \[{{\left( \frac{a}{\sqrt{3}} \right)}^{2}}={{x}^{2}}+{{x}^{2}}\Rightarrow \frac{{{a}^{2}}}{3}=2{{x}^{2}}\] |
\[\therefore \] \[{{x}^{2}}=\frac{{{a}^{2}}}{6}=\]Area of square |
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