Triangle

Area:

$= \sqrt {\frac {3a} {2} \left( \frac {3a} {2} - a \right)^3} = \sqrt {\frac {3a^4} {2^4}} = \frac {a^2} {4} \sqrt {3}$

Circumradius:

$= \frac {a^3} {\frac {a^2} {4} \sqrt {3}} = \frac {4a} {\sqrt {3}} = \frac {4\sqrt{3} a} {3}$