Step 1 :

Arc length of a polar curve :

Let f be a function whose derivative is continuous on an interval .The length of the graph of is from

is .

Step 2 :

The polar curve is .

Since , the curve over is a mirror image of the upper half of the curve over .

So first integrate from and multiply by 2.

Step 3 :

Arc length of the curve the polar curve is .

Let , then .

Thus, arc length of polar curve is 72 square units.