A) \[98\sqrt{3}\,c{{m}^{2}}\]
B) \[8\sqrt{3}\,c{{m}^{2}}\]
C) \[42\sqrt{3}\,c{{m}^{2}}\]
D) \[36\sqrt{3}\,c{{m}^{2}}\]
Correct Answer: D
Solution :
Since. All the sides are equal in an equilateral triangle. So, perimeter = a + a + a, where a is the side of equilateral triangle. \[\Rightarrow \]\[3a=36\Rightarrow a=12\,cm\] Area \[=\frac{\sqrt{3}}{4}{{a}^{2}}=\frac{\sqrt{3}}{4}{{(12)}^{2}}=\frac{\sqrt{3}}{4}\times 44\] \[=36\sqrt{3}\,c{{m}^{2}}\]
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