Question

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

Answer 1

Let x=18 be the side, then the height of the triangle is
\[h=\frac{x \sqrt 3}{2}

\]

Answer 2

The area is \[
\frac {x h }2
\]

Answer 3

Replace and you get your answer

Answer 4

\[
Area= \frac { x^2 \sqrt 3}4= \frac{18^2 \sqrt 3}4=81 \sqrt 3
\]

Answer 5

So divide 81 and 3 and that's my answer?

Answer 6

Also my answer has the PI symbol at the end so would that change by answer?

Answer 7

@eliesaab

Answer 8

Oh Sorry, I found the are of the triangle. You need the one for the circle. Wait a minute

Answer 9

okay

Answer 10

The radius of the circle is one third of the height h. So
\[
Circle Area = \pi r^2= \pi (1/3 h)^2=\frac {h^2}9 \pi=\frac{\pi}9 h^2
\]

Answer 11

Now
\[
h=\frac{x \sqrt 3}2\\
CircleArea=\frac \pi 9 \left( \frac{x \sqrt 3}2\right)^2
\]
Replace x by 18 and you are done

Answer 12

So 6 PI?

Answer 13

No

Answer 14

\[
CircleArea=\frac \pi 9 \frac { 3 x^2}4=\frac \pi {12} x^2=\frac \pi {12} 18^2=
\frac \pi{12}324=27 \pi\]

Answer 15

Thank you

Answer 16

Let me double check my computations

Answer 17

The answer is \[27 \pi
\]

Answer 18

Alright