Question

Find the area of a circle circumscribed about an equilateral triangle whose side is 18 inches long

Answer 1

If you draw this up and then draw from the center to the triangle angles you'll note that it splits the angles in two. We can solve for the radius using trig. We have a 30-120-30 triangle:
\[\sin (30) = r / 18\]
\[18 \sin (30) = r = 9\]
We can now solve for the circle are:
\[Area = \pi r ^{2}=\pi(9)^{2}=81\pi = \]

Answer 2

That last part should say = 254.47