Question

Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 6-inch radius A = sq. in.

Answer 1

$\bf \textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4}\qquad \begin{cases} s=length~of\\ \qquad a~side\\ -------\\ s=6 \end{cases}\implies A=\cfrac{6^2\sqrt{3}}{4}\implies A=\cfrac{36\sqrt{3}}{4} \\\\\\ A=9\sqrt{3}$