If side of a triangle is equal to the radius of circle having area of 154cm what is the area of equilateral triangle

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$$\begin{gathered} Given : Side of a triangle is equal to radius of a circle having area 154 c{m}^2. \\ To Calculate : Area of equilateral triangle with same side length. \\ Solution : Area of circle = \pi r^2 \\ \Rightarrow 154=\frac{22}{7}\times r^2 \\ \Rightarrow r^2=\frac{154\times 7}{22} \\ \Rightarrow r^2=7\times 7 \\ \Rightarrow r=7 cm= Side of triangle \\ So, Area of equilateral triangle=\frac{\sqrt{3}}{4}(side{)}^2 \\ \Rightarrow Area of equilateral triangle=\frac{\sqrt{3}}{4}(7{)}^2=\frac{49\sqrt{3}}{4}=\boxed{ 21.2176 c{m}^2} \end{gathered}$$

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