Question

Find the area of a circle circumscribed about an equilateral triangle whose side is 18 inches long.
a. 81
b. 108
c. 243

Answer 1

$The\ area\ of\ a\ circle:A_O=\pi r^2\ \ \ \ /r-a\ radius/\\The\ length\ of\ a\ radius\ of\ a circle\ circumscribed\ about\ an\\equilateral\ triangle:r=\frac{a\sqrt3}{3}\ \ \ /a-a\ lenght\ of\ a\ side\ the\ triangle\\-------------------------------\\r=\frac{18\sqrt3}{3}=6\sqrt3\ (in)\\\\A_O=\pi\cdot\left(6\sqrt3\right)^2=\pi\cdot6^2\cdot\left(\sqrt3\right)^2=\pi\cdot36\cdot3=108\pi\ (in^2)\\\\\pi\approx3.14\\\\therefore\\\\A_O\approx108\cdot3.14=339.12\ (in^2).....$

Answer 2

See attached for work.
$s=18\rightarrow r=6\sqrt3\rightarrow A_\odot=\pi(6\sqrt3)^2=\boxed{108\pi\ in^2}$