Question 281602
This problem looks fun!!!

You will have to visualize a square with a circle in it, the circle has 4 points, in which it touches the middle of every square.

The Area of a circle is:

{{{A = pi*r^2}}}

we know that {{{ A = 81pi}}}

so we get:

{{{81pi = pi r^2}}}
{{{81 = r^2}}} dividing {{{pi}}} on both sides
{{{r = -9}}} or {{{highlight(r = 9)}}} Since r is distance, we will only consider the positive value of r.

However, in the picture you visualized, you will see that the diameter of the circle is the length of one side of the square. A few more formulas!

Perimeter of a square: {{{P = 4S}}} where P is perimeter and S is the length of a side.

Diameter of a circle: {{{D = 2r}}} where r is radius and D is diameter

We get {{{D = 2 * 9 = 18}}}

and finally

{{{ P = 4 * 18 = 72}}} 
{{{highlight(P = 72)}}}

I hope this helps ;),
Bran