Find the circumcircle radius $ R $ of an equilateral triangle if area $A = 3$.

$R = 1.5197$

STEP 1: find side $ a $

To find side $ a $ use formula:

$$ A = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$

After substituting $ A = 3 $ we have:

$$ 3 = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 3 \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 12 = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 12 }{ \sqrt{ 3 } } $$ $$ a^2 = 4 \sqrt{ 3 } $$ $$ a = \sqrt{ 4 \sqrt{ 3 } } $$$$ a \approx 2.6321 $$

STEP 2: find circumradius $ R $

To find circumradius $ R $ use formula:

$$ R = \dfrac{ \sqrt{ 3 } \cdot a }{ 3 } $$

After substituting $ a = 2.6321 $ we have:

$$ R = \dfrac{ \sqrt{ 3 } \cdot 2.6321 }{ 3 } $$$$ R = \dfrac{ 4.559 }{ 3 } $$ $$ R \approx 1.5197 $$

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